Darn it,
Nothing, but NOTHING would get that nut off. I bought a 1 1/16 deep well socket and a 27 mm deep well, and neither worked. tried wd40, heating it with a torch, everything.
Option of last choice: I took a punch and a hammer, and sure enough I was able to drive it loose off the axle without too much damage. I hate when you have to resort to those kinds of tactics though. This was probably the first time in 8 years the nut had come off the bike...
I sanded out the conical well it sits in and sanded the conical side of the nut, added some moly grease and put it all back together.
Next time, it will come off easily, with regular tools.
PS; the brakes didn't look too bad!