White oak doesn't need a backing, as it is very strong in tension, and not great in compression.
Knox gelatin in not a great glue for wood to wood applications.
Narrow strips of bamboo can be placed side by side to form a wider backing, but it is really challenging. It's difficult to get them seamlessly staggered.
A backing is strongest when it's continuous from one nock to the other. It is possible to join them in the handle, but it may need a lam on top of it, and at least a stiff handle.
All in all, I can see too many hurdles along the road. I would advice you to change your plan.