Thanks to all for the helpful feedback.
As to why I like use sinew on Osage--I've found that when applied properly, it adds snap to the bow and protects the back, particularly when I'm added a reflex or recurve. I'm still a beginner bowyer, only made two bows so far, (selfbow and a flatbow with sinew), so as much as I pay attention to growth rings, the sinew is added insurance.
I think I will take everyone's advice and just focus on building a recurve, and use the bamboo in a separate bow on top of an osage stave.
Someday I would like to venture into composite horn bows--but that's a discussion for another day.
--Paul