the pillow case idea gave me an idea - if the hem on the top of the quillt is less used than the rest, we might be able to get a few 4 - 5 inch blocks from it to incorporate into the quilt back. And we can back those little blocks with another fabric so if they do tear, we may only have to carefully take the individual piece off - very carefully.
Thank all of you for verifying what I was thinking. It really helps to hear from people who have either experienced the old sheet problem or can imagine the same results that I do.