I'm no glue expert, but have used lots of TiteBond II and III on various household and DIY construction projects with wood, as well as PL Premium 400 construction cement on larger stuff. I think that in your case, however, you must also consider the oils that have penetrated that old stock over the years. I realize you can soak and dry it to some degree, but I still think I would go with an epoxy...probably the Brownell's Accuglass...and the pins. I had a buddy years ago who was very good at fixing those old doubles and he used Accuraglass and small wood dowels / pins. (The pins are just there to hold the thing together while the glue / epoxy dries).

Let me be clear that I have never personally done a repair like this on a old double, but I have done several on other stock pieces, splits and such. DFW will know, for sure if he makes it here.