oh yeah, i know all about adirondacks, especially blue ones.
It was on the arms that I used the beech dowels to cover the screws. I made a big effort to sand them smooth. By the time the chair was painted, the dowels were slightly proud and are very obvious when sitting in the chair due their height and their end grain.
I used ordinary upva glue on the chairs. 8 months in the blazing sun (yes, do have blazing sun) and heavy rain (we get that as well) and all are holding together perfectly
I since made something else and covered the screws with the type of plug cutter i listed, and they blend in perfectly.