Fleece is a somewhat tricky fabric to quilt with because of the stretch. It takes some testing and trial and error to get it right. It probably would be easier to put as few quilting lines as you can get away with, and that depends on your brand of batting. The shifting you see is in part due to the stretch of the bottom fabric. It very well may be easier to quilt it fleece up as suggested. I don't quilt with fleece or other stretchy fabrics, though others do. I stick to cottons.