Well, this is what I did: I pulled the layers apart. I tested it to see how sticky it might be, and found that the fabric wasn't sticky at all and the batting is a little bit tacky to the touch, but won't even stick to itself. So, now that all the layers are separate, I will take the tops and the backing fabric to Charisma for quilting, along with new batting. I believe I can still use the old batting to cut up for a rag quilt, pot holders, bibs or something like that. Those will be small enough for me to handle with my problem joints... :-D
Thank you everyone for your suggestions. Hearing them helped me be brave enough to just tackle the problem. ;-)