It gets yet weirder, but has a happy-ish ending. Yesterday I tried 3 browsers on my laptop and one browser on my ipad, none of which worked. This time, while I was on hold with the Delta agent as she was contacting IT, I tried Explorer on my laptop and also my ipad -- and both worked. I guess the moral of the story is that Delta's online system is currently incompatible with Firefox.

Go figure.