I like the idea of sewing a backing & flipping it to the right side. I've made a hexagon shape wallhanging and once I had it quilted...I decided I wanted it to hang firmly. I cut the same shape out of cardboard lay it onto the back of the wallhanging and then took another piece of fabric, laid it over this, turned the edge in ¼" and hand slip stitched it to the back of the wallhanging, I really like the way it hangs. I know it would be a little more complicated with your shape, but I think it is do-able.