You might want to stabilize the area from inside the tang inlet first. Take some sure thin crazy glue, soak the endgrain with the glue, put a piece of poly sheeting over the spot, and clamp. Let the glue set.
Then trim some wood from behind the tang so that the barrel can come back without popping the wood off. Stain the newly exposed wood.
You might also want to check that your pins have room to move in the barrel lugs. If not, file them oval to allow the bbl to move back and forth a bit.