Alright, got it out. There is a bolt with a rectangular head that sits in the battery tray, and the nut was stuck to it. I'm not sure if that bolt is supposed to spin or not... The bolt slides into the tray in a channel. I was able to get the nut/bolt positioned correctly to pull the battery up slightly, which locked the bolt into the channel, and I was able to break the nut that way.
Regardless, I have now decided the factory battery tray and hold down system sucks. Any recommendations for replacements?