With everything clean, I set about tackling what I expected to be the worst part: trying to wrestle the seat post out. Actually, it came out quite easily, and was not rusted at all below the tube line. Phew!
I put the seat back on, and flipped the bike over to work on getting the bent fenders, seized-up chain, and floppy front tire off. They were all getting in the way of moving the bike around, and I figured it would just be that much easier and lighter without them. The result is pictured above: a nice clean-looking bike, if I do say so! This is the last time for a while that it will look like this (i.e., all put together), so get an eyeful!
The next step is going to be cleaning up the front wheel, since it's in the best shape to begin with, and making some forays into working on the handlebars. I figure that will give me a nice boost to get started on the rear wheel, which is really a mess. I'm starting to think that it may not take as much work to get this beast rideable as I thought (knock on wood). Famous last words, right?