I called customer service, they're escalating it to billing, billing will call me, blah blah blah this is going to be a pain in the ass. I can't wait until we're off the grid.
(Gas heat is our only choice; we're in a rental. Well, other than portable electric heaters, which 1) would use a lot of energy, heating the whole place and 2) are specifically prohibited in our lease. Not that anyone is going to come check, but still.)