I was crazy enough to unpick everything I had done, peel off the backing, replace it with a lighter fabric and then rebaste the whole thing.
It was a big effort but I am much happier with the way the quilting looks on the new fabric.
Lesson learned: don't let the quilt shop lady talk you into a fabric you really don't want.
I'm not quite half-way through and so far I really only have one little section I'm unhappy with. I'm prepared to call it a learning experience and leave it alone.