I think this is finally solved.
A couple days ago when I was with a friend who was giving his opinion on the smell, shortly after I went hard on the accelerator, the battery light came on. I didn't mention that part because I thought it was just a dead battery rearing it's ugly head. The car seemed fine so a couple minutes later I turned off the engine, then tried to start - nothing but click click click. Battery juiced. Luckily we got a jump within minutes of me pulling over.
5 minutes later, the car goes into limp mode - all the dash lights come on and trans. failsafe. Got it towed home, had NAPA check the battery. It did have one bad cell so I bought a new one. Take it for a 20k test drive with new battery, things seem to be working well. During this time I can faintly smell burning plastic once the engine is up to speed, so I am driving normally and not any heavy acceleration since I don't want to induce the smoke again.
Later in the day I go for another drive, long story short after 60km the battery light comes on - then 5 minutes after that it went into limp mode. Luckily I was travelling at 80km which was enough to keep the car working, but when I stopped in town the gas pedal was no longer operational. I limped into a parking lot then called for a pickup.
After charging the battery again I got the car home. There is a whirring noise from the alternator area now, which was not present before, as well as the burning plastic smell - identical. With the car running at idle and 1500-2000 RPM the voltage was at 11-11.1. Not enough juice, alternator dead. Putting a screwdriver to my ear it sounded like clack-clack-clack in time with the engine.
So over the last couple weeks I have been slowly frying the alternator. I know of four instances where it was bad enough to bring smoke into the cabin, the first time I was on the test drive with the car, and the last when it completely died and stop charging the battery.
The PO actually just had the alternator replaced by BMW before I bought the car, so I'm hoping they might honor the 1 year warranty on it.
Anyone else heard of an alternator going this way?