I think the idea has some merit. I spent my career in the aerospace service industry and was tasked with finding safe and economical repairs due to design issues, corrosion, failures, etc.
I wouldnt dismiss the possibility of using some of the latest super epoxies or other products that have come out in just the past few years.
I have also thought of repair ideas that might be used to repair barrel corrosion and pitting.
We repaired some high dollar landing gear struts that had internal corrosion by machining the internal barrel of the strut and have the barrel chromed. Could this be done on a shotgun barrel? Im not sure.

Could a thin metal sleeve be hydroformed inside the barrel after back boring? Not sure.
Could a barrel be back bored and then heat the barrel in an oven, super cool the sleeve using methanol and dry ice then press the sleeve in for a interference fit? No bonding agent needed possibly eliminating the issues Teague experienced.
Wouldnt resolve the issue of making a dent non repairable but if you had a unserviceable barrel to begin with you got more time out of the barrel then you would have in the pitted state you are ahead of the game.