This will be a more long term completion, on account of moving in a couple of months. I see your points, though, and since I'm stepping out of my comfort zone I'll go ahead and follow the recommendations and wood back it.
Just for kicks though, as I was pondering, would sinew most likely twist, or otherwise skew, the limb tip alignment? After I posted the original question I got to thinking about the reflex pulling aspects of sinew. When it does pull the reflex would it tend to favor the weaker side more on an edge grain bow than a regular one? I was thinking it could probably make quite a mess of the tip alignment.