My grandmother and great grandmother made me a quilt several years ago that was a mix of cotton and polyester. It was a nightmare! For years, everytime my grandmother visited, she ended up doing repairs on it. It finally got to the point that it wasn't reparable anymore. It's really sad because they are both gone now.
As she was going through all the repairs, we discussed that in OUR opinion, the only help for it would be to go over every seam with a top side zigzag stitch to try to hold it together. We never did that - it was a king size quilt and a lone star pattern, so there were a lot of seams.
Good luck with however you decide to deal with this.
Carol B