Seems like a tall order, but doable. I've backed hickory with sinew- worked great. Jay Massey backed hickory with sinew with excellent results. But any of those backings should work.
A note. Once you pound it into finer threads, comb it with a brush made of brads driven into a small board. I didn't do this before, and got lucky the first time, but the last backing I did was uglier than I'd ever seen! It also was harder to lay down properly onto the bow's back.