Quote
my instructions are to "get the heat working, and disconnect anything illegal." I told him that the heat would be the only thing left working

LOL! [Linked Image]

It sounds as though somebody has done a lot of wiring without realizing how the 4-w delta system works, then later removed any receptacle which was found to have 208V (maybe after frying equipment?).

As for the heater, presumably it was working previously and was wired across two phases for 240V. Maybe it stopped working and somebody tried messing around in the panel without any idea what he was doing, then eventually gave up leaving the connections you found. Just my guess.