My mother recently gave me some heavy velvet drapes that she had on her windows for about five years (they were backed with blockout handstitched in the corners). Whilst the fabric looked unfaded and still plush it was terribly weakened. So I was unable to use if for quilts. UV light will destroy most fabrics, without them necessarily fading, so maybe that is the case here.
Erstan's suggestion is a good one, but maybe some extra quilting too. This may support the fabric and stop it pulling quite so much.
Will watch with interest, as I think this is going to be useful to others and maybe someone else has managed to find a good solution. By the way it's a lovely quilt.