Mike it right here. I'll take a flat sawn hickory back, for sure. The hard thing about quartersawn is there is actually no way to tell if the grain runs straight back to front. The lines are nicely parallel, and SHOULD be just fine, but that is examining the rings from the side. The radial grain could be doing what the heck ever it wants.
In Torges TBM series he shows how to take a large flat sawn board (4/4ths at least) and turn it into several blanks for kids' bows. He showed how ripping down the center of a perfect flat sawn board, with parallel ring lines on the faces, will give you several perfect quartersawn backings. That method is great. But, I have had several failures of backings, even with hickory and white oak, where I bought QS stuff that looked good, but which had radial grain running through diagonally.
I once bought a 4' long, 8.5" wide, 3/8" thick hickory board off ebay (advertised for scroll saw work) with perfect grain lines running straight and parallel the whole width of the board, back and front. I cut it into 2" wide strips, then ripped each of those into 1/8" plus thicknesses. The grain ran through fron to back on those that they snapped when bent just a few inches, before even being glued to a bow. The grain ran back to front diagonally in less than 1" through the 1/8" thickness.
Just saying, quartersawn isn't magic by itself. You gotta pay attention to how it gets there.