May I suggest, with the posting and two point, that in addition to dropping your heels you develop the habit of pronating the ankle.
Certain questions arrise when I suggest this, one of the most important the issue of relaxation. I think I addressed this earlier when I mentioned you pointing out the feeling you were relaxing right off the horse at times. Trust yourself.
One can not more ride a horse in complete relaxation than they can walk down the street doing so. The issue is tension, and relaxing and tensing parts of the body are just part of adjusting to movement and even simply maintaining and upright body.
There is no question that pronating the ankle and dropping the heel creates some tension in the lower leg, but just as some areas of tension allow other area to relax tension so does this.
So what is the use of it? I creates a locked triangle of stirrup treat, stirrup leather, lower leg. The small amount of movement needed to cue or adjust to very large movements of the horse can't cancel out this secure platform.
Like many new skills this can be uncomfortable while becoming conditioned to it. Your calf and achilles will have to relax and stretch, and that's likely to create tension for a time until the limits of stretch are reached. Then you can relax the calf.
The other area of the leg that will always be slightly tensed, in a good way, is the muscle that runs down the front of your shin, the tibialis anterior. It's the same one that is tensed when you drop your weight into your heel and lift your boot toe.
This muscle is the one, if underdeveloped, most involved in shin splints if I understand my human anatomy correctly. Mine is overdeveloped, even after 40 years of not riding in eventing and stadium jumping. A weak underdeveloped undersized tibialis anterior has a great deal to do with coming off the horse when you wish not to.
One modest sized muscle in the lower leg is the focal point for a good secure seat that is a comfort to the rider and to the horse.
At a certain level of development through use and conditioning it will stop being highly tense have the feel of just sustaining tension ... that is a feeling of preparatory flex for the coming movement, in walking, running, etc. On the saddle it remains quiet but helps maintain the angular lines that create the locking force for the lower leg to the knee.
But the pronated ankle -- isn't that a bad thing? Absolutely if you are on the ground running, walking, turning, etc. On horseback however it adds that one other angle of tension to create the sturdy and steady platform to post, to jump and land, to absorbe the impact of hard galloping.
You are creating a tiny three sided triangle down at the ankle joint, from the stirrup to the joint. So often we struggle with large muscle or large muscle groups to develop a better seat when this tiny little foundation is still not attended to. When it is watch your core strength suddenly come into play and your center stabilize. Want to rock your pelvis with the horse. Stabilize you leg from the knee down. Want to take the big jumps? Pay attention to developing this knee down configuration.
Why does it work this way?
If you are standing on the ground and roll your ankles outward, like a kid on iceskates for the first time, you risk sprain - and you can feel this easily. Don't push it of course if you do actually try it.
On the other hand, if your roll your ankles inward, the same kid, after fighting to get upright on iceskates will then drop the ankles inward, at a certainly point, due to the bone structure of the ankle, and bringing into play extremely strong tendons, so that the risk of strain is near zero. You can feel this easily by doing it.
It's not comfortable at first if you are not conditioned for it. The way my students practice it in the school is to respond to my voice request, "show me the bottoms of your boot-sole."
A nice effect, two in fact, then happens when this configuration is done. The knee tends to turn into the saddle, and the heel accepts more weight flexing more deeply.
The overall effect is to create a kind of iron triangle. Nothing much can move any further, so you can absorb shock in the bit of springiness that is left, which also allows you to have less loss of stability in sudden unexpected moves, meaning you will greatly increase you chance of quick recovery, or not even need to as you move with the horse without displacement of your center.
An unpronated ankle allows for a floppy leg that destabilizes under impact or pressure. Long before it can bring shock absorbing elements into play the opportunity is lost from too much range of movement.
Read the comments and watch the rides, or even study the stills of the great Olympic and international stadium jumpers.
It is considered by the best a personal failure, a riding and seat fault, if they ankles lose pronation during jumping. In fact you'll see that as they take their round during it's entirety they are riding with this leg and ankle position.
It is smooth, safe, powerful, and the horse loves it. It does so because the riders center moves far less over the horse's center. Must of the control of rider balance is felt by the horse as being directly over the fastening of the stirrup to the bar. Just, as I read your comment, you seem to be seeking as you fit and work on your saddle.
You may have learned this long ago. It's taught by many, and originated with first Caprilli the Italian captain responsible for the evolution from the backward seat (leaning back to take rough country and jumps), to the "forward," or huntseat. Vladimir Littauer authored some books that expanded on it more. Some riding groups, such as college teams in hunt country (Sweetbriar in Virginia I think it is) being one of them studied and learned from a contemporary and colleague of Littauer, and really perfected it.
I learned it from an employee of mine, a Sweetbriar grad, I hired to teach riding where huntseat had never been used before. The change in riding, the increase of safety for riders, the extent to which a horse could go increased immensely. I, her boss, mentored under her direction and instruction.
My own riding changed dramatically and later I went on to compete. I have never come off a horse at or over a jump. And the fews time's I've come off in other situations I was not fully in the saddle with this leg configuration. My last fall, in fact, I was half way up on Altea, and Bonnie in exuberant play was sure we wanted to all bump each other, and knocked me down. Had I been aboard I doubt she could have gotten me off even at my age.
The first horse I took on training, after 40 years of never having ridden, was a bolting shying funny but dangerous Morgan gelding. He did bolt a couple of times. I did not come off. He was used to people falling off him and not getting back on.
To end, it's only fair that I point out the conditioning necessary for this leg configuration as part of the seat. It's not easy but for most people it comes on pretty fast. With you, considering you have a problem ankle it not only may take longer but your doctor may advise against it. I don't have a solution for the latter possibility. I don't know the nature of your injury and could not comment.
You need to both stretch the calf and achilles, and tense the tibialis anterior. To do this stand with either a two by four under the balls of your feet, preferably with your riding boots on, our feet about a foot apart, more or less depending on your leg length. Drop into a soft easy limited two point stance and relax your weight into your heels, then pronate your ankles.
Do not do any stretching exercise to the point it hurts. Do not do this one until it hurts. Muscle soreness from exercise is okay but still don't overdo. At first holding for fifteen seconds will seem a long time. Keep building, very gradually, you ability to do this. I say, given the apparent area of your riding arena that when you can do a full circuit in two point in this position you'll have it down.
If you've already learned this before feel free to laugh at me for being such a pedant.
You will reduce your falling forward, and you will feel more stable, and it will allow you to post very low to the saddle, a more desirable way to post and the horse Diego will love you for it. High posting makes horses tense and crasy much of the time.
As to your saddle being part of the problem?
Likely you need to find a way to tip the seat portion of the saddle backward to level. Riding a dead level seat as part of a saddle is a learned skill. Without a front and rear rise to cup you into place it feels pretty insecure at first. It is like riding bareback, but that is the effect I think most are looking for with treeless. Time in the saddle is going to make a huge difference too.
That will require you to trust your body and forget too much direction and instruction (EVEN MINE) ... and just enjoy.
Donald, Altea, and Bonnie Cupcake