Oh, that thing is fucked. Feeling your pain.
The part that is spinning has a taper so it wedges into the axle carrier. Can you tighten it down hard and start over again?
That male thread looks destroyed/worn down. Was that rusted, or is it from 6 hours of struggle?
If you can't get the nut off, it may be time for a dremel and a stack of cut-off wheels.
Or, if you can just grind off the right parts of the base flange (of the nut), you might be able to get in there with a
nut splitter.