I see a problem with quilting any quilt that has been "birthed". If anything slides, you are going to have puckers or lack of fabric wherever that happens. Birthing works well for being tied though and so very much easier to correct if it isn't staying flat in the finishing.Personally I see no value in using batting in a quilt with a fleece back as usually the fleece is plenty without it. There are some quilts that I think are actually nicer with only the fleece as well as eliminating the extra expense of the batting. If you really want quilting, I'd do as pocoellie recommended.