Is there a "quick turn" method where the backing fabric shows on the front? In this case it would be sewn on BEFORE quilting.
I assume you'd cut the backing about 2" wider and longer than the quilt top. Layer the quilt first batting, then quilt top right side up, then backing right side down. Sew one side (raw edge to raw edge), shift the fabric, sew the other side (raw edge to raw edge), do the top (raw edge to raw edge), and the bottom, leaving an opening to turn it.
Turn it all right-side out...but you'd have to fiddle with the corners. Anyway, then you'd machine stitch around the seam line.
I'm making this up but surely it's done somewhere?