Buying from afar
Got started with a mini wire brush and some dielectric grease and now it works like new. Now I need to figure out the headlight switch and the door motors. 1 step forward...
You should just have one motor for the headlamps, mounted at the center of the car behind the grille. If you remove it and take apart the gearbox, you'll find contact points inside it that are operated by a plastic cam. Clean it out, steal one of the wife's emery boards, and file those contact points flat. It's very easy. Nothing even tries to fly out at you or out of place. It's a really simple design. While you're in there, clean and lubricate the gears.
Decades ago, I had a '72 Charger SE which used the same motor, or very similar (to the point of interchange). The doors worked but there was a horrible buzzing sound coming from the dash. Outside the car, when it was buzzing the doors were open, but vibrating like they wanted to close. I replaced the relay and nothing changed. I took the motor out and cleaned those contacts, and that solved it. Since that time, it seems that every headlamp motor I've dealt with needed the points cleaned.
I know they used that motor all the way through the 1983 Imperial, so replacements aren't impossible to find. While I don't think it's visually correct, I believe the door motors used on FWD New Yorker/Imperial work as functional replacements. The arc of travel on LeBarons may be too far, which might just require swapping in your gears.