The nut DID NOT need to come off.
A little mechanical persuasion brought the rotors right off.
I had the drivers side done in less than 45 minutes (including a quick lunch break), from wheel-off to wheel-on. The passenger side was a different story- I had more trouble with the bolts holding the Caliper Mounting Bracket than anything else. Ruined two 15mm sockets, used half a can of PB blaster, and finally ended up setting my floor jack up under the handle of the breaker bar and using the jack to break the bolts free.
After I got them out, the bolts had red powdery junk on the threads. I assume it was cooked-out loctite. The driver's side had this as well, but wasnt nearly as big a pain to get out. The brakes I just took off were the original brakes.
Anyway, re-assembled and test driven. The shake is gone.
Thanks for the advice guys.
Edit to add- I anti-siezed the hell out of all the contact points, maybe next time it'll go even quicker.