I would say you need to move your stirrup bar 1-2 places back. Stirrup bars need to be placed in the spot that allows the legs to hang with a vertical line from shoulders, hips, to heels, with the stirrup leathers hanging perpendicular to the ground. If the stirrup bars are too far forward it forces the rider into the undesired chair seat position. If the bars are too far back it pushes the rider forward and the knee will be placed to far in front of the stirrup leathers. If the stirrups bars are in the incorrect spot it prevents proper leg aids and the correct balanced seat. You want to sit in the deepest part of the saddle. You should have about a hand's width of space between the back of your butt and the top of cantle. The stirrup bar placement will help you keep your foot underneath you so you can have the ideal shoulder, hip, heel line.

First you want to find your balance. Place your butt in the deepest part of the saddle. Sit with your weight going evenly onto each seatbone. Right now you are sitting with your shoulders over your hips but you are not sitting on your seat bones and are tipping your pelvis forward. What you want to do is find your seatbones (which can be done by dropping your stirrups and lifting your thighs away from the saddle). You want your weight to go directly and lightly downwards on to the seatbones. So think of straightening your back and bringing your butt underneath you more. Remember to think of your pelvis as a bowl (Pelvis in Greek means bowl) full of water. If you sit with a swayback water will spill on your horse's withers but if you round your back and bring your butt underneather you too much you'll spill water on your horse's back. With your pelvis balanced your seat bones will help your legs support your body. This will help with the shoulder, hip, heel line. Now instead of arching your back to open up your shoulders just take a deep breath and just let your shoulders drop back and down naturally.

The foot rests straight in the stirrup with the ball of the foot firmly placed on the pad of the iron. It is best to ride with the feet centered on the pad of the iron.

Now the ankle is what makes the Saddle Seat leg different from all other english disipline legs. Unlike dressage which has a flexible ankle in Saddle Seat the ankle is stiff (this has an advantage that will be explained below).

I am currently in the process of writing a leg and foot position article. I just don't have the time right now to put it together but here is some of the research I collected. So read and let me know if you have any questions.

"Grip with the knees and the reply is to not to grip your knees, let me explain: knee grip or contact is certainly a primary necessity, but to command a rider to grip with the knees results in the riders pulling the knees directly into the saddle with the thigh muscles. This is a very tiring effort that results in rigid muscles that rebound from the saddle during posting and force the rider into rising strictly from his own effort. It bears repeating that posting is a movement that results from the motion of the horse, not a movement to avoid that motion. Of course you will see riders who go through vigorous posting entirely under their own power but they are completely wrong. In order to attain the proper knee contact which will permit the muscles to remain relaxed and workable, the position begins with the angle of the sole in the stirrup. This stirrup iron hangs at a slight upward slant that requires the foot to assume the same tilt with the little toe somewhat higher than the ball of the foot. Now in order to attain the necessary knee grip, we use the stirrup as a lever, and by swinging the heel slightly down and out, we find that the foot actually pushes the knee into position. This is assured when we realize that the entire leg worked as one unit from the hip joint and that the knee and upper leg roll into the flap of the saddle. So many riders try to correct out turned toes by twisting the ankles. Not only does this weaken the ankle buy it actually pulls the knee away from the saddle.

Here to watch that there is complete freedom of the knee to bend forward and back during posting. Often this idea of a single leg unit will be misunderstood, and the rider will "lock" the knee at the height of the post, which will result in his feet kicking forward while he is forced into the back of the saddle on the descent. The beauty of the knee grip through the foot position is that it permits the greatest economy of effort with a maximum of control and balance. Bobby Morrow, the great track star, explained his success as his ability to keep his muscles relaxed so that they are free to do their work. This is certainly true in riding as well as it is in any sport.

Just how far the rider should swing his heel to the side must be determined individually. Certainly the foot should swing out only enough to roll the knee and thigh into position. Swinging wider than that is an affectation that results in awkwardness and ugliness. A good personal check for the rider is to glance down the side of his leg and swing the heel down and out until he can see the entire side of the leg down to the sole of the boot. To check the foot for the forward position it is generally practical to say that the stirrup leather hangs at a right angle to the ground. Feet forward of this line will swing back under the stirrup hook at the height of every posting movement to cause the same swing that a locked knee will cause. There is a well known phrase in riding, "the seat must be independent of the hands." Certainly this is so but such phrase needs a lot of explanation for the young rider. Literally it means that we must have such good posture and balance in the saddle that no matter what awkward motions the horse may go through we will be able to keep our balance without hanging on to the reins to maintain it. It also means that our hands must be so thoughtful flexible and adaptable the any head movement by the horse taking care of by the hands and will not pull the body out of position.

From the front it may look too “flared” but from the back one can see that the leg is correct because the calf really is not far from the sides of the horse. 

Without losing form or shape bring calf to horse and begin to squeeze with whole leg with most pressure coming from calves.  Remember the Saddle Seat leg is a single unit from hip to heel.  So when giving leg aids there is only lateral movement of the knee to bring the calf in for pressure, there should be no turning of the leg or from the ankle.

It is clear that balance and control seat and hands are very dependent upon each other. Balance starts with the foot in the stirrup and like the old spiritual, "the foot bone connected to the ankle bone the ankle bone connected to the shin bone, etc.," your entire body balance depends upon the feet in the stirrups. Happily, if the foot is right in the stirrup the knee will be right. If the knee is correctly placed into the saddle, the thigh will be snug. If the thigh is snug, the seat will be in the right place in the saddle. So, you see, your position is truly built from the foot up. How very important it is that we realize this!" (54) (Crabtree 50 – 54)

The rider should place the ball of their foot straight across the stirrup iron so that the toe is pointed straight ahead.  If the rider’s toe is not straight ahead, his weight is not being properly driven into the iron, which will cause his leg to swing unsteadily. 
The stirrup leathers should be in a vertical position when viewed from the side. The rider must push his weight onto the stirrup irons, but not onto the heels, to place them in such a position, which will not only give the rider a more secure seat, but also help to relieve the horse’s back.  
A common error is to hold the leg in this position by gripping hard with the calves and pivoting from the knee at the posting trot and canter.  Not only is this improper, it also compromises security as the rider is "perched" precariously on the top of their mount. 
While the leather should appear to be vertical from the side, it should not be vertical when viewed from the front. The thigh must be pressed flat against the saddle, therefore pushing the rider's weight into the leather and altering its position. 

http://www.geocities.com/Petsburgh/2070/ezine/discipline3.html

Saddle seat riding begins with a balanced and centered seat, sitting in the deepest part of the saddle. Your seat should be squarely under you, with your weight distributed through your seat, down through the inner part of the thighs and through the heel. The heel of the foot should be down and outward, which puts the knee and thigh in a close and comfortable contact with the saddle. The heel should be lower than the toe. The foot position should be almost directly below the hip joint.

To obtain the proper position, the rider should place herself comfortably in the saddle and find her center of gravity by sitting with a slight bend of the knees without the use of irons. While in this position, the leathers can be adjusted to fit. Irons should be placed under the ball of the foot with even pressure on the entire width of the sole and center of the iron. The foot should be in a natural position, being neither extremely in nor out from the horse's barrel. The stirrup irons should be just below the ankle bone when the rider's foot is out of the stirrup and the leg is hanging naturally against the side of the horse. Holding the stirrup at about a 15 degree angle and having the rider place her foot in the stirrup; will help her to attain the proper leg position.

http://www.joannemacbride.com/saddleseatarticle.html

"Before considering the foot position in the stirrup, it is advisable to take a look at the stirrup itself. If the stirrup is held close to the horse’s body, the pad is parallel to the ground. However, the only way for you keep the stirrup in this position would be to wrap the lower leg around the horse’s side, thus opening up your knee and bringing your thigh away from the saddle.

When the stirrup iron is pulled away from the horse’s side, the inner branch of iron becomes lower than the outer branch, causing the bottom of the iron to slant downward and in toward the horse. When your foot is placed in the stirrup, it is of utmost importance that the foot assumes this same angle, making the big toe lower and closer to the ground than the little toe. The foot should be placed in the stirrup tread so that pressure is evenly distributed across the full surface of the stirrup. This is accomplished by having equal pressure across the full width of the sole of your boot.

This leads us to the age old question of whether the rider’s toes should be turned in or out. Most beginners ride with their toes sticking out. As you improve, the toes should gradually turn toward the front. However, you should not be instructed to "turn the toes in". For 99% of riders this would be very unnatural and uncomfortable. (Most people walk with their toes pointed slightly outward and when riding the legs are spread on either side of the horse’s body, exaggerating this position. Watch your own feet the next time you walk, and as you keep walking spread your legs further apart to see what that does to your toes.)

When you are forced to turn your toes in there maybe disastrous side effects. It can cock your ankle out, causing the inner ankle to become cramped while straining the muscles around the outer sole of the ankle. This will destroy the natural function of the ankle joint and the Achilles tendon, which allows for leverage between the ball of the foot and the heel cord. It is this flexible leverage that allows you to stay balanced on a high-action, animated horse. Without this flexible foot action, the reins will very often be used as a medium for maintaining balance instead of as instruments of control, collection and flexion.

The lower leg position that bothers me the most is the knee pinched in so tightly that the lower leg is propped out like a wing. This position usually causes you to turn the toes inward, with all of the stirrup iron pressure only on the part of the ball of the foot that is behind the little toe, with no pressure on the ball of the foot behind the big toe.

If a rider is forced to turn the toes in, putting extreme pressure on the little toes, they frequently become numb. Not only does it become impossible to use the leg aids correctly if the toes are turned in, but the rider will rarely develop a secure seat. (Please note that I did not say gripping against the saddle. Good relaxed contact with the knee on the saddle is desirable, while a stiff, gripping knee acts as a pivot and causes the lower leg to swing out too far.) A gripping knee about the diameter of the horse’s body will tend to push you up and out of the saddle. Also, a gripping knee will become stiff and will lose its flexibility which is necessary for relaxed, balanced riding. The most effective way of staying on the horse is through contact with the upper calves below the diameter of the horse’s body.

Toes that extremely turned out are also undesirable, especially if they are accompanied by gripping calves that are constantly squeezing the horse’s side. This position can quickly drive the game, sensitive horse insane and is the cause of many a runaway. However, forcing the calves away from the horse’s side (seen with the toe in ankle out foot position) is just as bad. The knees are forced into a locked position and the lower leg is so far from the horse’s side that the leg aids are delayed. Also, when the legs are that far from the horse, it often startles him when they come in to initiate a leg aid. Some horses might be frightened by a simple leg aid used in an effect to merely help guide him. The upper part of the calf should rest in a relaxed fashion against the saddle and never be forced away from it. The lower leg is useless and out of place if it doesn’t hand in such a manner that only the slightest squeeze inward touches the horse’s side and receives an instant response from him. If the rider’s lower leg is placed unnaturally, the rider can only maintain position and balance by extreme effort, producing stiffness and rigidity.

In order to be a secure rider, it is also very important to ride with your heel considerably lower than the toe. With the foot in this position you will be a lot less likely to lose a stirrup, plus the foot will have less chance of sliding all the way through the stirrup. If your heels are up, the result is slack useless calves, but if your ride with the heels lowered, the result is harder calves that can quickly and energetically communicate with the horse.

It is very important that the rider’s muscles be allowed to work naturally. When the foot follows the lowered inner angle of the iron, the leg muscles and the ankle joint are allowed to work efficiently. This position also causes the thigh to lie flat against the saddle where it should be, with the inner thigh muscles stretched down, helping to place the knee comfortably against the saddle. This natural position of the foot not only looks better, but is also more functional. Joints and muscles must operate smoothly and easily in a natural way before the rider can be effective and graceful. Riding form must be functional before it can become beautiful. It should be remembered that it is the legs that create the movement from the horse. The legs create the impulsion that the hands must then collect and guide." Gayle Lampe

Lets review

Do not force the leg shape. Let your weight stretch down and out through your ankle. This will roll your toes in so they are parallel with the horse, create the correct foot/iron angle (15 degrees) so the weight is on the ball of the foot and away from the pinky toe (it also helps to bring the big toe to the top of the boot and the pinky toe to the bottom). Another tip is to try to put your knee cap on the saddle. This is impossible but it helps bring the ankle away from the horse (and if you have the correct weight distribution in the iron it won't flare your calf away from the horse which is undesirable). To bend your knee and bring your foot underneath you bend from your knee like you are kneeling on the ground. Your stirrup bars should be adjusted so your knee is bent and your foot is underneath you. When in the saddle you do not want to push your heel down so hard as to push your foot in front of your knee. Or don't try to bend your knee so much so you heel is up and you forget to let your weight sink down and out through your heel. You just want your heel lower than the iron. Remember like in any disipline you want that straight line from shoulder to hip down to heel. Don't think of your weight in your heel and in your seat to stop at the horse think of in going down to the ground and under the top soil.

To test if your feet are in the correct spot while in the saddle stand up in your irons without using your hands. If you fall down you need to make an adjustment. While standing straight up in the irons and you feel like you are falling forward your feet are too far back or if you feel like you are going to fall backward your feet are too far forward. Now when your feet are balanced underneath you standing in your irons will be as easy as standing on the ground. Another way to think about it is while sitting in the saddle if the horse where to poof! disappear how would you land? If your feet are balanced underneath you you should land flat on your feet but if your legs are too far in front of you then you would fall on your butt or if they are too far behind then you would fall on your face. Have you ever done squats? Think of sitting in the saddle like doing a squat. You need your legs underneath you to keep you balanced and your leg muscles are what hold the weight of your body up.

I also noticed that you post like a dressage rider. In dressage and hunt seat the rider’s position and the horse’s movement have the rider’s hips swing more back and forth towards the withers while going up with a loose lower back.

In Saddle Seat the riding position asks the rider to use their back as a single unit and "the hips should stay under the body with neither a mechanical up and down motion nor a swinging forward and backward."

With the height of your horse's head I would keep about a 90 degree angle with your elbow. Space your hands about horse's mouth width apart with point your thumbnail toward your face and press your whip on your horse's shoulder.

Since you are used to sitting up too high on the saddle sitting correctly will bring you farther away from the horse's neck. Because you have shorter arms and with the height of your horse's head you will have to ride with a little longer reins. This is ok as long as you do not ride with your hands behind pommel.

Good posture, sitting with weight going perpendicular to the ground, ears lined up with shoulders, shoulders lined up with hips.  As a rule do not let your toes go past (as in front) your knee.