OK, here I go for about the hundredth time, DON'T USE GLUE, use shellac, the best sealer out there. Easy to scrape off when you start building a bow, clear, you can see the condition of the back(did I take that stave down to one ring?), dries in 10 minutes so multiple coats go on quick and easy.
So, here is my experience with white wood glue;
Best osage I ever cut, arrow straight, flawless, knot free, removed the bark but not the sapwood, coated the backs and ends with multiple coats of white wood glue, placed staves in an out building. About a month later I checked on my staves, every one was checked from the back to the belly, huge checks you could drop a quarter in and all was now firewood.
My not removing the sapwood played a major roll in my woods demise but trusting wood glue
played an equal part. No more wood glue for me me since and no more bad checking.