I've used Titebond III (waterproof) with sinew and the results are very springy and water beads on the surface. Just use the Titebond III like you would hide glue: size the wood with it, use plenty of glue with slightly damp or dry sinew, and put a layer of glue over the whole job when the sinew is dry. Not primitive but it works.
(I'll probably get flack for this but, yeah, I said slightly damp or dry sinew. IMO, too much water messes up the job.)