I put it into gear and it dies.

ok, i will try and clean out the connections starting at the easiest to get to then I will try again with the bulkhead.
I'll be working on it the whole 3-day weekend so hopefully we can get ALL the issues so far solved.
the big one still being it not wanting to drive.
That connector on the column is pretty critical. Do that first since you know its a problem.
Do you know how those round terminals are held in there? and how to get them out and reinstalled?

Here's the thing about a poor connection on either the J2 (run) or the J1 (feed) wire.
a. resistance causes heat. You just experienced that! LOL
b. A voltage drop in those lines will cause the voltage regulator to see a low voltage when the engine is running. It will then work to bring system voltage up. Then you'll have an alternator running at 15.5 Volts, and if the connections to other stuff like the battery and headlights are good, that's what they'll see.