Have you tried turning a sock into a sleeveless sweater with small arm holes. I once cared for a dove who chewed her back. While She was with us she wore her little sweater which was secured with a bow piece of sock on back and we had alternates to wash and wear. When she healed we would give her time off for good behavior and put the sweater on when she would start to chew again. We just threw up our hands and accepted that she was going to wear that sweater and kept redesigning and improving the fit over time. She ate and played and was a normal dove after she realized it was her second skin and it was not going away so she could chew. We did try to play more and redirect her attention , but she had to be alone when we were at work etc.
There is no perfect answer. You will find it revealed in tour heart. Bless You,