As an update to last night's entry: I slept in the living room again last night, and slept fairly well. Not a good long-term solution, though.
Thanks to all for the supportive and helpful comments. I should've noted that I already do everything within my power on the physical side. For example, as soon as this started I went back to wearing earplugs while sleeping. I'd done that for years, finally stopped around the beginning of this year (I was sick of my ears itching all the time) and discovered that I could sleep fine without them; that lasted 'til the end of March, when this whole noise thing began. The car is loud enough that it wakes me up despite the earplugs—no other car in the lot wakes me up even without earplugs.
(Someone told me the other day that the huge "muffler" on this car is probably actually a noise amplifier; it's probably not "just the way [his] car is," as Loud Car Guy told me in our confrontation a couple weeks back, but rather a deliberate choice to make the noise as loud as possible. I don't know enough about cars to know whether that's true, though.)
I also take an assortment of sleeping drugs (NyQuil, valerian, occasionally alcohol, once in a while a leftover Sonata), but for me any given sleeping drug becomes temporarily entirely ineffective after I use it one or two nights in a row, and they're often ineffective if I'm too tense (even though I suspect part of what all of them do is relax muscles). I've been listening to relaxing music before bed, and after waking up at too-early times, and it's helped some but not enough. I've been trying Heather's suggesting of stretching before bed, when I remember to; that, too, helps (a lot of the problem is sheer physical tension), but not enough. I'd like to be able to run white-noise, or even music, all night, but my apartment walls and ceiling are very thin, and I would hate to wake up my neighbors.
The problem is exacerbated by my general difficulties with sleeping: for example, I've never been good at falling back asleep after waking up (another skill I need to learn), and I tend to have a hard time sleeping in a new bed (so occasional nights in the living room may not work).
Greg suggested talking to corporate management. I confess that I'm extremely uncertain about who exactly owns this apartment complex; there's a management company that the guy I'm calling Apartment Complex Guy works for, but they're extremely flaky and hard to contact. There's a woman who might or might not be the owner of the whole thing who comes by to oversee maintenance sometimes, but I don't have any way to contact her directly; I don't even know her name. And the hint that I should move was subtle enough that I suspect Apartment Complex Guy would simply deny it.
Sadly, I can't just park in the space myself (but thanks for the suggestion, Jon!). That's what I did a few weeks ago, and it resulted in the big blowup that made things seriously worse. Also, there are two spaces that he commonly parks in that are right near my window.
I've also considered trying to move to another unit in this complex; unfortunately, I think most of the likely options are on the side of the complex where the narrow exit driveway is, and where presumably the noise would be significantly worse. Of the three buildings, one has bedrooms next to the parking lot, one has bedrooms next to the exit driveway, and one has bedrooms that front on the street—but that last might still be better than where I am. I should look into that. (It even occurred to me that I could ask to keep the same apartment number and have it moved to the new door, but it was pointed out to me that that would cause all sorts of difficulties. But I thought it was an elegant solution, in an impractical programmer kind of way.)