Barracuda died on lift at exhaust shop.

Not sure if battery was disconnected or not. Guy was supposed to be the best custom exhaust guy in town. He owns many old cars himself, so I would assume he knows what he is doing?
If "he started it several times on the lift", the battery wasn't disconnected. Not every vehicle is wired like these old mopars. I figure you have a problem behind the dash (amp gauge, weld splice, other), whether welding caused it or not. Good luck