Ken,
I am not sure how it would with a synthetic head, but I have my friend head their dunun with either using rope instead of a second ring (just using one length of rope tied slightly smaller than the circumference of the ring and then a second round with loops knotted for your verticals to go through), and I have also seen it done with no metal rings at all, so that it sits tight around the body of the drum. One length of thick cord was used in the place of the ring, the skin folded back over it, then holes punched through both layers and a second cord above that with loops being pulled through to the underside to create loops for the verticals.
I can try to find pics or a better explanation if you car. Again, I have no idea how this would work on a synthetic head
good luck