If I were to use fleece for the backing (and I like the idea of not sliding around for a lap quilt), I would heavily starch the fleece before making the quilt sandwich. This would keep the fleece from stretching when you machine quilt.
My recipe for heavy starching is to mix a solution of Sta-Flo liquid starch 1:1 with water and paint it on the fabric with a wall painting brush. I toss the fabric in the dryer, then iron with steam. This makes a fairly stiff fabric that is *not* going to stretch!
Although I haven't used fleece for a backing fabric, I have used it for a pieced top. I'm really glad I starched the fabric heavily before cutting. All of the blocks came out to size and went together very easily.
I think starch is an underused produce among quilters!
Mary