New shoes. Appear to have the same clearance off the upper control arms as stock tire size. At full right lock in reverse the passenger side tire was just touching the wheel well liner. A few seconds with a heat gun and I was able to push the edge of the liner back an inch so there's plenty of clearance now.
Did a little messing around with a jack this morning to check clearances. I suspected that at full droop the tire might make contact with the upper control arm. Things were very, very close:
I'm not a fan of wheel spacers, but decided that I'd like to have the extra 1/4" of space a slip on spacer would give. From what I can find the general consensus is that if you can still get 7 full turns of engagement out of your lug nuts there's no concern with this small of a spacer. After adding the 1/4 inch spacer I was able to get 9 full turns out of the lugs. Will running wheel spacers cause the truck to explode and the universe to end? I guess we'll see.
The clearance at full droop after adding the spacer was much better:
A quick run around several local back roads revealed no odd vibrations or shakes. Nothing is rubbing on the well liners or mud flaps. The Cooper Strongholds ride very smooth with just a slightly higher amount of road noise over the Uniroyal street tires that came on the truck.