I'd hate to misdirect you, but bamboo is very strong, and it doesn't take much to hold a back.
As to the draw weight, maybe it would make weight, but otherwise you probably already know you can......... A. shorten the bow. B. re-glue with more reflex. C. add a very thin lamination between back and belly lams (maybe even just a power-lam and tip wedges, depending....) or D. wait until you get the backing you want. Up to you since you are there doing all the work.