Ghostrider, loading a pieced top under it is an idea. I've never done that and am not sure how it would work, dealing with the smaller piece on bottom instead of on top. I don't think it's the weaving of the fabric, because the dark spots are definitely where the fabric is drawn up.
Tartan, I'll try boiling a little bit of the fabric. If that fixes the problem (without ruining the color of the fabric) then I might be able to put the whole thing in a really big pot and boil away. Double double, toil and trouble. Fire burn and caldron bubble.
Thanks for the ideas.