It might, you'd have to experiment with an instructor watching to tell you if it makes a difference. Sometimes it just cramps your leg up and actually forces you to shove it backwards even more, but it doesn't hurt to try.
You have a lovely horse. Try lowering your stirrups a hole or two so your legs are more around your horse's barrel. For many of us, it is challenging to stop jumping for our horse, jumping ahead of their motion. One trick that I learned when jumping is to focus on the top rail or part of the jump until you cannot see it anymore through your horses ears. This helps finding the correct distance to the fence which, in turn, should help you to wait for the horse to jump up to you. Best of luck!
Leg position comes from your overall position. Core strength also plays a role. Sit back and relax. These size jumps you should only have your bum out of the saddle 1/2 an inch. You are jumping for him anticipating the jump. If he is a safe jumper set up a gymnastic with xrails. Drop your irons and sit. Close your hip angle just a bit over the jump but his natural jump will push you up enough in the saddle to hold it. What for the landing and sit. Your leg is going back because you are standing in your irons and pushing off them forward over the jump. Don't lay on his neck either. The neck is used for balance to help out riders from becoming off balance not a resting place. Each hand should be on the side of his crest with a light hold not laying on him. I disagree with needing a larger horse and that's what is wrong with your position. You would have these same issues on any size horse. I am 5'7 and use to jump a 13.3 pony that did not change my position at all from him to my 16h eventer. Use ground poles to work on sitting and closing your hip a bit finding your release and putting weight in your heels. Make this a habit do this until you are bored to tears. Train your body the correct position and it will translate to the actual jumps.