How big is the quilt? I used fleece for the backing on a lap-size quilt once and it worked just fine. I didn't use any batting as I thought the fleece was warm enough and lofty enough without it. I do remember that I basted the heck out of it because I was afraid, like you, that it would stretch. It wasn't that bad to quilt but I didn't do anything fancy and kept the quilting to a minimum. That was before i had my LA so I did it on my domestic.