Hickory would be a good backing.
Bamboo is fine, too, but Jeremy has experience that many of us do. The best boo-backed boofloo's I did were tri-lams glued up in two stages; backing and core glued in pretty decent R/D profile (lots of reflex) and then glued again into a more moderate profile when the belly was added. This takes best advantage of the Perry reflex principle.
If you have vert lam boofloo, you can also rough tiller and then pull it into a mild reflex with a thin hickory or fabric back.
Keep the bow a little long, since your blanks are not all that wide, and make the tips stiff, narrow and deep. Boofloo bows shoot very softly in the hand and are really smooth to pull, if tillered right..