Sleep? Never touch the stuff
Latest car-guy update: building management has worked out a compromise with him, whereby instead of parking 20 feet from my window, as he was doing for a couple weeks, or 30 feet from my window, as he's done this past week, he now parks 10 feet from my window. I'm unconvinced that this is an improvement. (It's conceivable that it is, because it might mean that when he backs out of his space, he won't be changing direction 2 feet from my window.)
Unfortunately, the only way to determine whether it's really a problem or not is to see whether it wakes me up. Which isn't going to be very feasible if my other sleeping problems continue. Last night I was asleep by 1 a.m., and woke up at 6; a major improvement over the 1-hour-at-a-time of the previous two or three nights, but still not sufficient. So I was already awake when he left, and I couldn't tell if it would have been loud enough to wake me. The fact that his idling engine made my bed vibrate (I tried to make that phrase not sound like something from a bad chromepunk-porn story, honest I did) is probably a clue, though.
Also, there's a different guy from the apartment management company involved now, and he sent me email the other day that hinted that I was the one who was causing problems by not respecting my neighbors and by attempting to take matters into my own hands.
I suspect that the reason I'm not getting enough sleep (and that usual assistants like NyQuil and valerian and even that Sonata I had prescribed a couple years back aren't helping) is that I'm too tense, and that part of why I'm too tense is this car situation. Unfortunately, I also tend not to sleep well in unfamiliar beds, so shifting to my living room might mean not sleeping for entirely different reasons. But maybe the thing to do would be to sleep in my living room for a week or two until I can get back into the habit of actually sleeping, and then see if the noise problem goes away.
It's all very discouraging.