Thanks guys - success!
The idea that worked was to drill a small hole in the center of the square nut, and then use progressively bigger drills to get to 1/8. I then reversed the drill bit and put it in the hole, held it with a hand vise and simply undid the bolt. I noticed I had drilled a bit into the bolt, and so I'm not really sure if it was the drilling that freed it up, or the ability to hold the nut tightly, but either way, it worked.
Now I have a nice hole to put oil into the threads if I have any future issues!