UPDATE: the tractor is coming home tomorrow. Here's what transpired over the last week or two. The dealer also sells LS tractors and someone from LS contacted them recently and said they've had a few instances of their tires spinning on the rims and they issued a bulletin on what to do to fix or alleviate it.
Guess what? TYM uses the exact same rims and tires on some models, including the 2515. The dealer took my wheels and tires and put them on another tractor, added some counterweight and lo and behold, the tires spun on the rim.
So after the dealer spent a lot of time and effort tearing into the tractor to throw parts at it, they found out it was the tires spinning on the rims after all.