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