Don't know if this is a good idea or even a practical one but what about putting a layer of warm and natural and then sewing on a new backing, leaving the old backing in tact and then maybe quilting on the quilt lines that are already there. Sounds like an awful lot of work to me but thought I would throw that out there. Good luck. I'm sure that someone much more experienced with quilting than I will come up with a much better idea.