This seems to be my major mistake. I should have made the board thicker, glued the handle on, then cut the limbs to thickness.
Exactly how thick is the bow in the limbs? What's the thickness of the original board, minus the glued on handle, in the grip? You might still have enough thickness for a light weight bow.
Either way, I wouldn't leave this bow as is and start another one. You're already nearly done, and you might get lucky. Worst case scenario: the handle pops off violently, the bow breaks and you still have to start another. But perhaps the handle pops off slowly, so you can replace it with a longer handle, composed of several 1/8" lams instead of one thick block.
By the way, shorten that long string until it is nearly touching the handle. It'll give you a more realistic view at the tiller.