Finally solved this one. I had to use Replay Media Catcher. I still don't know the stream URL (if there is one) but RMC did record it correctly. The first try, it stopped about halfway through (about 188 MB) but when I increased the RMC buffer, it finally captured the whole FLV file. TMPGEnc converts it into MPEG2 and I can now burn it to a DVD.
