So after moving some stuff to another partition to make the apps happy again (the complaints were from things that more or less continually overwrite their config files) I noticed that it wasn't just that the partition was full; it was filling at nearly 400K/s
du -h --max-depth=1 | sort -k 2 > readingone
(wait a few seconds, so that df -m showed at least a 3M discrepancy)
du -h --max-depth=1 | sort -k 2 > readingtwo
diff readingone readingtwo showed that just my home directory grew, not any subdirectory.
ls -ltr showed no files currently being written, which seemed wrong to me. lsof | grep /home/username stalled for a moment, and I saw a really big number for just a second.
ls -altr showed the culprit... .xsession-errors It seems that Azureus was throwing exceptions at an insane rate... the file got up to somewhere near 1,682,654,466 bytes before I flushed it. (That number is from lsof since one program still has a file handle open to the purged file)
Moral of the story: when something is going crazy and filling up your hard drive, don't forget to include hidden files in your listings.