Bouvier,
As Rocketman said, cutting out the bulge is not practical. However, this kind of damage could be repaired a couple ways.
One way would be to sleeve the barrels. This would involve cutting the barrels off a about 3 inches from the breachface and boring out the chambers to a larger diameter. New barrel tubes would be turned down on the back area to match the bored out chambers. The tubes would be soldered in and the outsides blended to the original barrel section. Ribs would be reattached and the barrels blued.
Another way would be to work the bulges down with hammering while a mandrel is in the bore. If the bulge is in the forcing cone, this could make it more difficult to cold forge the barrels down correctly.
