I'm sorry to be among those voices for completely taking it apart; but having done this several times myself, I believe you (and they) will ultimately be much happier with the finished product. Fay had the right objective when she mentioned inspecting the seams of the original piecing.....so many issues point to someone who probably did not know what they were doing, so you can assume there may be issues with the seaming, too.
If you have to go all the way to individual 5" blocks, don't despair, it *will* be worth it in the end. It'll take you maybe a day or two to take it apart, but could frustrate you for several days to try to finish it like it was started.
You could replicate the quilting stitch design on your machine and cut down on your time *in* that way, too.
What a precious thing you are doing for your friend. You and she will always remember it and both be warmed by this quilt.
Jan in VA