Voltage regulator smoking?

We through alot at ya tonight.
I might tackle it by begining with following the circuit from the Battery positive to the key switch. Check all those junctions and the condition of the fusible link.
Check the line from the alternator output to the inside. The welded junction is wrapped in the harness and probbaly fine. I'd leave it wrapped unless you have some reason to have to check it.

Then go investigate how the regulator and alternator got wired up.