One consideration here on TIG- no matter the welding amperage, nor the parent metal-you stand a good chance of putting the barrel at the breech "out of round" and heat transfers always to an open or thinner area of the mass- so if the soldered top and bottom barrel ribs fall into that classification, the heat input from a TIG (steel 2% Thoria electrode ground to a blunted tip)electrode might do that. I am assuming the barrels were packed in a seperate section from the receiver-stock group, so that the dent is only on the barrel breech face? UPS will "nit-pick" every damn claim they can, and I wish you mucho bueno suerte here in dealing with them. One thing you might have going for you is that your "damaged" Arrietta is still a production gun, so the price of a new fitted set of barrels as well as the selling price is fairly well known- as opposed to the value on a set of, let's say here, "Roadrunner" steel barrels for your uncle's AHE 20 bore Parker..