This is a challenge. If hung on point, will any of the fabric be straight grain, up & down? If not, I think it might sag over time. So I think the foam insulation board is a good idea. It comes in 4'x8' sheets, so it could be cut to 40" sq. then the quilt could be tacked frequently to avoid sagging.
I saw a round quilt with a flange on the back. A piece of PVC pipe was connected into a circle that fit into the flange.