So you want to rip off a 'backing' from a board, and glue it to the same board back again?
That...well...wouldn't be a backing. It's just a laminated selfbow then. No matter what you do, the grain will not get better on the back[ing] in some magical way. There's just no sense in cutting an iffy grained board in two and glueing the two halves back together,
except for the fact that this allows you to clamp the blank into a reflex and/or deflex shape and hold its shape. Instead, if you have a poorly grained hickory board, back it with a good grained hickory lamination, from a second board. One good hickory board may yield four backings to save four iffy grained boards, used as belly.