Hi Rich, in my previous lives, I was a service manager in a large boat shop... we worked a lot with polyester and epoxies, and every one on the planet has worked with super glue... Cyanoacrylate.... But, the very best adhesive for your task may be just commercial grade wood glue??
From the net...polyvinyl acetate (PVA), also known as "white glue" or "hobby and craft", and aliphatic resin emulsion, commonly referred to as "carpenter's glue" or "Yellow glue"
Both would provide a bond stronger then the surrounding wood... But if your really serious... some type of long setting epoxy would be the strongest.. the weirder the mixing ratio, the better the Epoxy... Epon mil. spec. was the strongest I ever used... polyester, not so good, very little penetration and will fracture easily... Good luck, til...lat'r...GT...
