Just a few comments. Don't know if any will be relevant...
1 - Unlike a lot of folks, I see nothing wrong with riding with the foot mostly thru the stirrup. I asked the question on this thread not long after I joined HF, but most of what I wrote then still applies. Question on stirrup position: ball of foot or mid-foot (home)
2 - I am very slowly building more flexibility - slowly as in 4 years and still with a long way to go. However, when your heel is under your hip, it is harder to lower your heel. When it is under my hip, slightly lower than level is the most my heel will go down even if I try to force it while sitting still.
Some people consider it very important to have the heel under the hip. I don't, so I find moving my feet slightly forward (or better still, riding in a saddle that puts my feet somewhat forward) makes it much easier for my heels to go down.
3 - If you are nervous about losing your stirrup, then you will tend to put your feet further into them & make heels down harder. Our Appy is pretty level headed and I find myself riding with my stirrup at the ball of my foot. My mare still sometimes does the sideways jump or sudden reverse, and I unconsciously put my feet much further into the stirrups with her.
4 - Shorter stirrups make it harder to lower the heel. If I'm standing, I can raise my toes no problem. If I bend my leg, then the backward tilt of my lower leg uses up all the flexibility my ankle has to offer. Sitting folded up in a chair as I type, if I put my heel under my hip, my heel WILL come off the floor.
5 - If my boots have a leather sole, they tend to slip more in the stirrup & I tend to stuff my feet further in. Rubber soles on rubber pads makes it easier. I once tried leather soles on stirrups without pads, and it was slick as snot on a doorknob. I spent the ride with my feet jammed thru the stirrups.
If none of this helps, ignore it & someone else will offer better advice. I find riding involves a lot of trade-offs. Trying to force my body into the "correct" position is a lot like forcing a horse into the "correct frame" - it makes things worse. I started riding at 50. And I'm a guy. I'm not a 14 year old girl who can twist her body like a soggy spaghetti noodle. Just like a dressage horse doesn't get there in a year, my body needs time as well.
As regards conditioning my body, I honestly have more luck just riding than trying to do stretches or exercises. It is kind of like throwing a ball. Exercises can make your arm stronger, but there is no substitute for just doing a LOT of throwing. Also, a 2 hour ride does more to improve me than 4 rides of 30 minutes each. On a longer ride, gravity and the horse wear my body out, and I stop subconsciously using my muscles to resist the horse. After 30 minutes, I still look tight. If I get off then, I don't make much progress. After 2 hours, I ride MUCH better.
In weightlifting, it is the final repetitions that give the most progress. In teaching my horse to ride trails, I notice it is the second hour that gives her the most progress. And so it is with my riding form.