Sinew backing makes woods compress LESS, not more.
Second, I'm convinced a lot of bows that look like they failed in tension actually failed in tension when they break. Set is absolutely an issue, but whenever I can't ID another cause like a bug hole or a nick, I wonder. Whenever I see a fret, you can see also that there is a subtle kink or hinge, and that angle is where the back will get over-strained and pop a sliver, and it goes in the next second.
NOW, I was literally on this exact track once and let me tell you what I found out. Tim Baker was right, design is king. I was convinced that if I got super strong backings (bamboo), and super strong belly woods (ipe, bullletwood) that the back would never pop and the belly would never crush and we'd all live happily ever after. I bought brazilwood, granadillo, greenheart, massaranduba, jatoba, coyote, Peruvian walnut, osage orange, ipe, kingwood, pau-ferro, ebony, tropical bamboos, etc... and they all worked, but there was NO super-wood out there.
ANY WOOD CAN BE BACKED. It's all a question of balance, limb width, trapping, and design. I have seen red eolm backed with bamboo. I have backed hickory with bamboo, etc...
Woods offer compressive STRENGTH, and compressive ELASTICITY. Bamboo offers tension STRENGTH, sinew offers tension ELASTICITY. The really important thing is figuring out how to best use the qualities.