I'd explain to the customer the difficulties of using polyester and the problems you're having. Tell her to get something more appropriate or take the quilt elswhere. She would end up with an unsatisfactory job, and you will likely get bad publicity from her, not to mention frustration for yourself. I use a lot of sheeting with 20%poly & 80%cotton with no trouble, but one with 80poly was terrible. That quilt developed lots of pilling as well. Your lady would find it hard to get any LA'er to tackle this
Wish you luck