The tape "pancake" that came apart on January 1: Over the past week I finally overcame my dread, and in three separate sessions, spent about seven hours unknotting it (with white cotton gloves on) and putting it onto a reel.
Then I baked it again (because it had been more than a month since the first time), and tonight I transferred it. It sounded quite good overall, though some of the levels on the tape were a bit too hot and there was a little distortion on some peaks. Fortunately it was a 15 ips recording, which tends to help conceal minor amounts of physical damage a lot better than 7-1/2 ips. And it was Dolby "A" encoded, which prevents print-through from being a problem most of the time.
Before and after photos are attached.