I imagine cutting out the thin sections, then welding in a new piece of sheet metal, is rarely cost-effective unless minimal shaping work is involved. Good assumption or no?
On another note, I saw a Punjabi guy stop a friend's tank which was leaking along an inch-long crack that developed on a friend's bike, using lye soap, jute-fiber string, water, and a flat rock. He cut the string up into short frayed bits, mashed it into the soap with a little water on the rock, and kneaded the mixture till it looked like a big pink booger. Applied to the tank, and it sealed and held. (Apparently the soap reacts with the gas...?) One of two times I was impressed by ad-hoc repair skill in India. (Second time was several days later when he bent friend's pipe back into place with a long, stout stick which miraculously came to be his hand, in the desert at the very site of our minor crash...)
Held like a champ through a week of rough riding in Rajasthan, and seemed poised to stay in place forever, at least until the rainy season...