It's bad times. I think my hot end is broken.
So the first problem is that the thermistor came loose from it. I noticed part of the black silicone gel came away from it, and at closer inspection, the thermistor seemed to have come away. The black part of it anyway. I replaced the black silicone, and it seemed to be working ok, at least for one test print.
After 2 days at it, the hot end is heating up just fine, but that's about it. It's not feeding right, even after I've thoroughly cleaned it, and I've now got no idea what to do. Things are looking grim.