Don, Center shot is not necessary for a good shooting bow. If you have a correctly spined arrow you can be just as accurate with a simple, relatively wide handled Eastern Woodland style bow as you can with a center shot bow.
Self bows can successfully be made with cut out arrow shelves but an added on shelf would be more durable IMO. A bulbous handle, as per Torges, will give you a sturdy handle and with a small wedge of leather, wood, antler, etc you have the best of both worlds. I prefer to use a Ferret's floppy rest.
Adding an overlay can help stiffen the handle area but if that area bends at all, the overlay will probably pop off. Pat