I ran the uninstall a second time, only when it got to that same dialog box, I went to shut down the computer. That didn't even display an error or anything; it just wouldn't shut down. So I went in and terminated the five instances of msiexec that were running, and then I could restart the machine. When it came back, I just went in and manually deleted the several hundred meg of files that were still there.
Now it's complaining about Adobe Reader, which shouldn't've been affected, but frankly, that's ok, because I was going to replace it anyway, with the Foxit Software PDF reader program that I'd been using since forever, but somehow got strong-armed aside by Adobe at some point.