Well, I finally replaced the battery today.
I'd left on the same damn cabin light again yesterday, and today the car would sort of start, but not go into Ready. I got various error lights, including the battery indicator. Weighing my options, I got out my multimeter and checked the voltage on the replacement battery (still sitting on a table in my garage) -- about 12.6V. So maybe it was OK? But I still had to get the old one out.
Long story short, I ended up breaking off the top part of the positive terminal cover (the part that folds back), accidentally -- but it was good, because I could finally see the post clearly enough to see that there really was nothing else holding it on; it was just stubbornly stuck, and I'd be OK to pry it up with a screwdriver... and, having resolved that, I suddenly didn't have to, because it came loose after a bit more wriggling.
To my surprise, after changing batteries, I didn't lose my radio station presets, as I had before.