Ya know, Hedgie, I been wondering that myself for some time. I have never heard of it or seen it, but that does not mean it will not work.
I think the problem will be in how some of the sinew is thicker and stronger than other areas, hard to get a consistent tension and it may mess up the tiller really badly. But since you are using your own sinew and stave, and not one of mine, I will "let" you try it out providing you post your results here!