as sniper said, the back matters most and vertical or bias is preferred over flat because if you use a flat sawn backing, especiall of a ring porous wood like red oak, there is always some runout that exposes the weaker early growth to the back surface where the tension is greatest and the rings can separate (lift a splinter). diffuse porus like hickory maple or birch is not so bad
in the case of a pyramid bow where there is no taper in thickness, keeping a flat taper when you tiller/scrape is a pita if you are working in and out of the soft early growth.
As I recall, mr stanley's designs do not call for much tillering on the bottom so sanding with a board backer or some kind of planing will work out better should you choose a flatsawn belly of red oak
BTW, I have not seen Mr Stanley around lately, can you say where you saw him presenting his work?