The back of the bow is very humpy-bumpy. Unless you're working with Osage, it could be quite the challenge and I fear that it wouldn't hold up. Also, let's face it; it is deflexed quite a bit. Most white woods even if starting out very straight or even with some reflex will end up with an unacceptable amount of string follow when completed. However, I know what it is like to have a piece of wood calling to you. How about this...
Instead of chasing a growth ring to establish the back how about squaring or flattening the back as best as you can and glueing a hickory or bamboo backing to the stave. Prior to gluing the backing of choice, push the bow "board" into a reflexed position. Then apply the backing while the board is in the reflexed position. You can build a clamping jig to accomplish this. When the glue dries, it will maintain its reflexed state. Continue with the tillering process to make your bow.