Could you cut a one inch strip of fabric, fold it in half completely. Then cut your normal binding width for a straight folded binding (I use 2.25 inch). Fold this in half as well. Layer the one inch strip on the front of the quilt, so the raw edges touch the raw edge of the quilt, then layer the binding on top of that, again with raw edges touching the raw edge of the quilt. Sew your 1/4 inch seam all around. This catches all the raw edges. Fold over ONLY the binding edge and hand stitch to the back, leaving the smaller piping on the front. With the one inch piping strip, you'd get about 1/4 inch of piping showing on the front.
Would something like that work?
Rachel