I looked over and over at your pictures trying to see what seems "off". I think it is that your knee is locked. You have multiple joints in your body , useable to absorb the horse's motion, but since you are locking up in the most important one, your knee, the foot then becomes overloaded. Too much pressure directly down into the heel, which is pushing the stirrup forward.
If you can relax a bit more at the knee and ALLOW your leg to follow more closely, in a draping manner, along the side of your horse, there will be less feeling of Force into the stirrup. You can see how the whole lower leg comes off and sticks out stiffly to the side in some photos.
I think part of the reason this happens is due to the shape of your hrose. My guess is that he has a nice big barrel and porportionally narrower shoulders. The half draft that I ride is shaped this way. What this does is make it hard for me to keep my lower leg from drifting forward into the kind of "groove" area in front of the girth. What I need , in order for me to be able to be stable and not fall behind the motion, is to have my leg under me, and I need my knee to kind of accordian up and down some (of course it doesnt move, but rather opens and closes) . Also, think about "aiming" your heel back, toward the horse's rear feet, ratther than straight down to the ground.
The more impulsion you can get from the hrose's hind forward, the easier it will be for you to achieve this.