Ta-da!
Tire issue sounds like alignment problems (duh), which I had with the Cube. Tried shims, which were a janky-looking fix, but they worked. Any alignment shop should be able to do them. When loaded, the rear alignment changes significantly due to the rear suspension design, and wedge-shaped shims at the hub bring it into proper alignment.
I'll do some more looking on this end... doesn't match up with any of the info I'm familiar with, but between the two of us, we should be able to figger it out!