The side cover gasket is still a much larger project than I wanted it to be, but it's not quite as bad as the bottom gasket. The side cover butts up against one of the transmission mounts (the old ones, because - thank Providence - the new ones have STILL not come in), but instead of having to take off the entire mount, I just got to remove the broken bottom half. Then out came the cover.
Absolutely caked with grime, of course. Now, I also pulled out the lever seal, and after some searching, found a replacement from Fatsco. Wonderful folks over there. They also had replacement bolts with crush washers already installed, which was great, because I couldn't find this size washer anywhere else. (For those unaware, the side cover has 13 bolts, of which the bottom 5 are under the fluid level, and so require crush washers. The other 8 bolts are not, and only have lock washers.) The seal and bolts should be here in a week or so.
When that's done, I'm going to replace the drain plug seal, and hopefully that will end the Saga of the Leaky Transmission. Then it's back to the windshield wiper hookup - which I think I've finally cracked - and the a/c.