I tried multiple different approaches (front of the tire up first, back up first, etc), but on mine a 255/60/19 will not fit with the tire fully inflated and the hitch in place
. I removed the shields which bought me a bit of room, but the tire is still pressed up against a part of the underbody/frame.
I don't have the key to remove the hitch so the tire is currently just hanging a bit lower than OEM size. I'll likely deflate the tire once I acquire an air compressor to keep in the vehicle capable of properly inflating it.
Hard to see here, but the back of the tread is caught up on part of the frame: