The more I think about it the more I truly believe that surface on the back needs to be sinewed into a flat smooth surface.I can't get around the fact about the tension lines will be intermittent too much not sharing the tension load properly.A recipe for disaster.Wrapping with cotton strips after sinewing gells to make it flat with no air left in dips.I'm not sure whether all black cherry staves from all black cherry staves have these undulations.
Possibly just rawhide can be put on the stave with smoother back with sapwood on.
Also a person could possibly do very good getting a very clean edge grain board to back with rawhide.