I had a Navy Arms upland 12 gauge years ago that I had traded into. Before shooting it I took it apart, and discovered a split vey much like you describe. I wedged the split open, and filled the split with Acri-glass, and then removed the wedge, and secured the split with a large wood screw. The screw stayed, and was hidden under the barrel tang. This being said, I wouldn't be quite so confident, had the gun been an antique, with the likelihood of some oil saturation, and being a 10 ga. to boot.
As for restocking it, unless you have crazy skills, skip right over this idea. I knew an old gun builder, that build beautiful longrifles. He decided to build a double shotgun for himself. His family still has it, and swear that project is what killed him.
Hungry Horse