Yep, soppernate's right. URAC is really outstanding for wood to wood applications, yet it is pricey and more laborious to work with. Save it and use Titebond III, which excels in applications like applying backings of rawhide, snakeskin, paper, fabric, etc.
Regarding "overpowering..." The back of the bow undergoes tension and the belly undergoes compression when drawn. In between the belly and back is the neutral plane that basically "goes along for the ride." This is why some glass bowyers can use foam cores in the their limbs, because it's not really doing any work. Also, the lighter a limb is, the faster it can recover. Now, if you put a backing on that is considerably stronger in its ability to withstand tension (i.e. boo, glass, etc) than the belly is able to resist compression, the belly will succumb to the forces and fret, hinge, and/or take excessive set. The opposite is also true. If a belly is incredibly resilient to compression (such as horn, glass, ipe, boo, etc), then the backing must be able to withstand the added stress or it will fail. Hope this helps. It's been a LONG day at work and I'm not completely coherent.