I’ve taken to backing some of my quilts that are less than 60″ to a side with a brushed knit fabric. It’s called Minky, Minkee, Blankee, Soft n Comfy, Cuddle and who knows what other misspelled versions of fabric names wholesalers create, phonemic awareness be damned. There are printed versions, versions with little bumps, and versions with different amounts of brushing, pile length and pile curliness, but I like the plain smooth best personally.
I quilt it on a long arm quilter. (I’m not sure how one would quilt it like this on a sewing machine – I don’t think I could, because the fabric stretches one way (across the width – which can be controlled with careful measuring and pinning to the rollers of a long arm) and no amount of diligent pinning without rollers would anchor this down right for either hand quilting or sewing machine quilting.
Be careful. Once you go down the soft plush back path of quilting, everyone that currently has a quilt will want an upgrade to the plushy kind.