I battle the same exact thing. The Martin side plate materials works good, but it wears out too quickly for me. Black Widow sells the perfect material for me. It looks like velcro, but it much softer. It brings my arrows dead center. I can't shoot a bow correctly without it.
Go to their site, and look up item # 320. They call it "recurve shelf rest and side plate" material.
Try it, I can almost guarantee it will move your arrows over. If it doesn't, let me know and I will buy it from you.