There are a number of posts on QB of people who have used fleece and Minky on the back of their cotton quilts. You might be able to read about their experiences if you search out some of those threads. The soft fabrics are wonderful to touch but sometimes not so great to sew but pin well and use a walking foot. Pull on your yardage to see which way stretches more and use that way for the width so you will have fewer problems. I would suggest leaving out the batt because it will be easier and it will be warm enough without it. I say go for it and you can give us an update on how you make out.