I've used Elmer's wood glue on many projects without a problem.
I would have to question the bedding and general stock fit! That seems to be an old well-used stock and from what I read from another rifle. Why fix it yourself? Take it back and have it done right!
Boyd's make a great stock and your action/barrel may fit right in, but I wouldn't just install it and call it good. They benefit from proper bedding. I have an At-One stock under a custom Argentine Mauser and found their relief cuts very generous.
Though the At-One is a good adjustable stock, the fit and finish leave a lot to be desired.
