@jadmt was correct. The 35x11.5R17 Toyo AT3s did indeed rub ever so slightly. On this particular JK, it was the front swaybar. Rear seemed to have plenty of room. We installed the 12mm spacers and everything seems clear the normal items. Misses the frame by a few milimeters at full turn/stuff, but misses.
However, as AEV warned in the instructions, you do have to trim the OEM Hardrock rockrail. It misses during any normal street or easy trail work, but it can hit at full hard stuff in the rear. We'll end up trimming it an 1".
Will continue to update the thread as more data is gathered.
Oh, I have to say, the Toyo AT3 seems to be the perfect overland tire. Not an AT, not an MT. The hybrid style is as smooth as any AT I've ever tried, but seems to have much more bite in the dirt than most ATs. The Tire review can be separate thread