Have you considered sewing it on like any regular quilt binding? In retrospect, trying to sew that satin binding on by hand might be very interesting. I h.a.t.e how satin moves and slides. Years ago, one of my daughters insisted on a satin dress for a school dance. That fabric made me crazy! Would your quilt lend itself to having something like giant rick-rack or a playful thin binding as an applique over your stitching? There are some cute thin laces that could be sewn to cover your original stitching. Wouldn't really work for a boy.
Another thought..... What if you deliberately ruffle it?