Put clean mouse traps (that snap) on the top of the quilt , maybe on top of tissue paper. We did this with our Great Dane dog on our sofa. He did not get on the sofa after the first few tries. Put a clean sheet over the top. Shut the door if you can to keep the cat out. Or shut your cat in another room when you have a quilt loaded. I wouldn't undo the quilt. That's a lot more work than repositioning the cat.
Not to be alarmist but this sounds like a very good way for the cat to get a real injury. I'd recommend deterring with foil/plastic bags some texture that the cat doesn't like to sit on.