When you cut away the damaged ends, you may be able to salvage some fabric, to use to re-inforce the weak and worn squares, simply by hand-applique the matching square over the old one. (one fabric at a time). Google "Quilt Restoration and Repair" and Ann Wasserman (AnnQuilts.com) has excellent advice and technique. Hey, you may have yourself a new special skill when you are through with this one! TAKE PHOTOS of your steps! for your own reference, and to demonstrate your talent and care with potential clients!