It's just a weird game, because they don't really need to leverage AH against Chicago. They only need to leverage the state against itself. It's not like AH has the ability to back something like a bond offering the way the city can with the hotel tax (at least in theory). Yea they need to get into the nitty gritty of a property tax assessment deal, but they really can't do that without a more concrete plan that provides some benchmarks that the taxing municipalities can set a development offer upon.
It's either entirely for optics, they actually want to stay in the city, or some 4D chess operating I can't comprehend.