I don't think the polyurethane glues such as Gorilla Glue are highly visible in a joint. Actually, in my own tests, they do very well in a close fitted joint, even better than clear epoxy. But the foam-out into the surrounding wood shows up under the new finish unless you can scrape or sand away the foam-out mess. Used inside of a stock where the joint wouldn't be visible, they might do very well, but I would not use them on an exterior crack. The shelf life is horrible too, and I've thrown away much more than I've ever used.
I like Titebond II for the most invisible joint in wood that isn't oily. If your stock was heavily oiled and blackened, I really doubt if you got all of it out, and it will migrate back to the surface over time. For this reason, any glue repairs should be done fairly soon after de-oiling. The polyurethane glues are recommended for oily woods, but they are very messy to work with. Epoxy is also good if the surface is free of oil, with thicker epoxy such as Acraglas Gel being better for filling larger gaps or cracks that cannot be pulled completely closed. Of course, wetting the wood to pull the cracks closed will not work with epoxy. KY Jon is probably correct that normal atmospheric humidity will migrate back into the wood to close the cracks that opened due to excess drying from the solvent baths. But it will be a horse race, because oil deep within the wood will also be coming up to compromise the glue joint. Considering that the wood may be weakened due to the long term oiling, and the harsh organic solvents, you may be wise to strengthen the inletting and head by soaking it with a cyanoacrylate glue.
