If you are going to re-bind the quilt, how about blocking it with the binding off? also because it is wool, you could try blocking it with steam, tailors re-shape wool cloth with steam to stretch and shrink different areas of jackets and trousers to get them to mold to the body. For best effect (in tailoring) steam and press the area to shrink, under a pressing cloth! then to prevent the cloth from getting too hot, swap to a block of wood to use instead of an iron and press down with this until it is cool, dry and set. It requires patience, as it can take longer than you think for, for the fabric to really cool down again.
It goes without saying, but I will say it anyway - have a practise on a sample similar to your quilt first, I don't know the affect that steam will have on the quilted wool/cotton combination, but I do know that wool is great for molding with steam for garments.
Good luck
Rosemary