Fleece on the back? Why not. As you said, it's stretchy but that isn't much of a problem with such a small quilt. I have put cotton, fleece, flannel, whatever. Once I had a piece of lavender brush tricot stuff that I made the front just to fit. I also think of adjusting the fabric type and the thickness of the batting to where the baby will be when it's small. Northern Montana VS Southern Texas. I raised my babies in WY, so I was used to lots of warmth, thick, flannel. I'm making a blankie for a "someday hopeful" for my daughter in Phoenix. It will be thinner and cotton.