Have you tried a pillow behind your back? I am short and if the seat of the chair is too deep, I have to move my body forward in the chair. Most times I don't need more than an inch, so I have a very thin pillow that I use. I bought a throw pillow at WM and took out one of the two inserts in the pillow, because it was too thick with both in it. That puts me sitting me in the chair perfectly.
Try with a towel first to see if this will help. Or fold a quilt so that you get support from it. Hang as many as you need to get comfortable so they don't slide down and see how much you need to be moved forward in the chair. Then make a pillow. Or leave the quilt there?
FYI.....I have to put a throw pillow behind me on most couches, otherwise blood flow is restricted to my legs. The seats are just too deep for my short legs.