August was only scheduled to run for a certain time period and they wanted to make it an open run, but Billy Elliot was already scheduled to start MAJOR renovation work on the subbasement of the Imperial because of the two-leveled set that needed to rise up from the stage. August was doing very well at the time and it was economically wise to switch theatres.
Chicago and Steel Pier did share a producer (PACE Theatrical Group, who seem to have been a pretty big producing force in the 90s, with Tommy, the revival of Grease, and the Dennehy revival of Death of a Salesman amongst their credits). I would hazard a guess that whether they went into this revival with the Weisslers already knowing that Steel Pier was coming in or whether that happened after the fact the discussions to move Chicago over to the Shubert were very amicable.
(Side note: even though Big flopped in there pretty quickly, I forgot just how long of a run Crazy for You really had there)
Shows used to move more often because the laborerers who would take down sets could be paid very little. That's why out of town tryouts used to be more common. A famous example is with Annie Get Your Gun, in which the sets were too heavy for the Imperial walls, so within two days they were starting a third out of town tryout while the Imperial was being reinforced.