I use TBIII on the last course of sinew on "Elkie" the bow in the article I wrote for the latest PA. I use it to hold down where the sinew lifted from the bows back too. They are compatible and should work fine.
I believe with hide glue, you can heat the area up a bit and the glue will become soft and you can wrap the area down until it dries. I've never done it but I read it somewhere. If this is the case, you won't have to add another component. Pat