No guarantees but here is what I done. Obviously the sinew is glued together well, so why not use it ? The bad bond was between the sinew and the wood. I scrubbed the wood with steel wool and acetone, scraping off the big hunks of glue. Let that dry well. Then I scraped the whole bow with a section of saw blade, really ruffing up the surface. I then wet the bow with a spary bottle of warm water, just a light misting. Let it soak in a while. While it is, mix up some glue. Use whatever you used on the sinew the first time. Make sure it's mixed right. I use a small pack of Knox in 1/4 cup of water and nuke it for 20 sec in the microwave. Your micro may be different just don't let it foam up. Now reflex the bow until it will mate up with the sinew . I tied mine down in the middle of the handle with twine and put wood blocks under the tips till it lined up. Once that is done sze the bow wood with hide glue. Just brush on a light coat end to end and let it tack up. Now bbrush on a thick coat of glue on the bow wood and the sinew. Make it heavy. Now line the two up and pinch them together in a few places with spring clamps, while you get busy wrapping with elastic. Ace type bandage from the Dollar Store works well. You might want to put a pc of wax paper over the sinew to save the elastic from sticking too much. As you do this you will see glue oozing up thru cracks and voids and holes in the sinew. GOOD ! This fills them but more importantly creates a good bond. Wrap it up and put it away for about a month and a half. (you can remove the wrapping in a couple of days) But don't screw with the bow for a month and a half. You've introduced a lot of water to the wood and it needs to dry out before handling. During that time if you see any edges that need attending you can work some glue up under them and rub them down while the glue dries.
Worked for me on a 50" hickory Modoc/Hupa type bow. 50# @ 26"