This happened yesterday, but I was busy. Happy 4th, by the way.
They are now saying it is a bent rim (good call, petrified rabbit). It either happened earlier and they missed it twice, or it happened in between when the car was barely being driven. Either way, I ordered a new rim and will hopefully have it early next week. I found a shop with a road force and will have them put the new tire on since the dealership obviously doesn't check things properly. They checked my other three wheels and things seem fine with them.
So it seems I had more than one issue. The ruined tires, bushings (which they stripped the bolts trying to remove them) and now the rim. Hopefully this will be the end of this.