Pat, I'd suggest that you remove all of the sapwood as I've heard that sinew will pull the sapwood from the heartwood as it dries. matter of fact that happened to Manni Ebner- I sent him a couple of ERC billets that he sinew backed, only to have the sapwood pull free.
Ever since I've been wary of trying it.
heck, I have a bad enough time with sinew pulling the heartwood apart
,,especially belly cracks which won't hurt performance but sure do look bad..