The only currently available technique I hold out hope for is some form of spray welding to restore the barrel's interior to solid, uniform steel.
I know of no currently available spray welding process that could be used inside even an 8 gauge bore. 12 gauge or smaller would be out of the question. I've seen a couple different spray welding processes in use, and the size of the equipment, and the requirement that the arc or plasma spray be applied perpendicular to the surface being repaired, would preclude filling even one pit inside a barrel, let alone lining and restoring an entire bore.
Spray welding isn't even used to build up and resurface worn out ways on lathes, because it will delaminate at the thin edges when surface ground or scraped. The molten metal droplets spread out and stick to the surface, and to each other. But there is not the same type of fusion to the base metal as in other welding processes where the base metal is actually melted.
Then there is the little problem of the heat generated during the process. Even the lower temperature arc and combustible gas processes would heat the barrels hotter than the melting point of the solder used to join double barrels. The plasma spray process, which would give much better adhesion and a more uniform surface, is much hotter than that.
Maybe someone will someday miniaturize spray welding equipment to the point that it could fit inside a long small diameter tube such as a shotgun barrel. And maybe someone will also develop a process to inexpensively 3-D print a new set of barrels that would perform safely. Right now, both ideas are nothing more than dreams in the distant future.
