I'm not sure why folks are assuming I'm going at this as "this might be an issue, replace"; I'm going at this on a "do research, ask questions, get feedback, start working on the things that would be beneficial even if it's not the exact problem, test, continue". If fuel is boiling, that's a problem, so might as well do something about it. If it's not a problem (or not "the" problem), then doing something to make sure it doesn't become a problem isn't exactly a bad thing, and it rules out one potential issue. I know I don't know much about motors or diagnostics, so as I'm doing more research I'm asking questions. Asking questions does not equal just running out and replacing things. To your questions:
I have not checked the timing yet. I just got the last part for the fuel lines last night so hope to finish that up today.
I tested the alternator with a multimeter and it's fine; it's showing 14 on the gauge and similar at the battery. The old alternator was definitely not charging as I tested it the same way. Again, I keep coming back to the alternator because the problems started immediately after I replaced it, and that was the only change that was made. Still, I totally understand that one does not necessarily equal the other.
The engine does not start at all after it dies. It turns over very strongly but will not start for a solid 2 hours after the fact. After this most recent failure it wouldn't start for well over two hours; I ended up pushing it back into the garage and starting it the next morning, though it took quite a pull on the starter before it fired.
Ultimately I think under hood heat is the ultimate cause, but since the car has gotten hot before I think it's affecting some other part. Someone had suggested the coil before, and it sounds like you might be in agreement with that possibility.