I like the look of unwashed cotton once it is washed in the quilt. Will the poly not shrink and will the cotton even shrink if the water is not hot? I did the burn test and it is most definitely poly.

Okay so she said she would still like it and she was the one to offer me more money, so it looks like I'm going to going to buy some stabilizer, any suggestions for the stabilizer?

Before you iron something to the panel, how about making a sandwich of the thin panel, some NON-ADHESIVE interfacing and a light weight cotton and do just enough quilting on this sandwich to insure you have a more sturdy piece in the center. I'd be scared witless to iron anything onto the panel itself.