I use Titebond 3. That stuff is unbelievable...but I am a novice CBG builder...but it has worked great on every wood project I have ever done, including the fretboard I just glued on my second CBG.
My pick is gelatine glue (no joke). do a search for "oyster glue" here on the nation. It's an alternative to hide glue. Like PVA glues (carpenters or wood glue) it can be removed with heat/water but makes a great bond.
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the best,
Wichita Sam