Chris here... tried to start the engine, and, par for the course, it won't turn over. We've tried about 10 times so far. We turned on the generator, and it seems to want to start with the generator going, so we're going to let it sit for 10 more minutes and then try it again. If it doesn't work, we have a spare brand new starter that we're going to swap in. We have some leeway on time - right now, with conservative speed, we're supposed to arrive in Charleston at 1:30pm or so on Saturday, so we can afford a few hours of waiting for the moment. Let's hope that it's not tooooo long.
Update: Replacing the starter... let's keep our fingers crossed that solves the issue. It's highly unlikely it's the battery - our generator starts fine off the same battery. Soooooo... an update when we have one.