Agreed. To call it a theater is a stretch. Essentially it is a flat concrete pad with rails for the floats, temporary style bleacher seating, and a steel beam octagon or pentagon shaped structure erected over the top of it. I think the tech booth is essentially a shipping container that would seem easily moved as well. Of course, this is all wild speculation, but it seems like a pretty simple.
Rough guess here, but IF they wanted to do it cheaply and were just going to re-build it as is without any modification, the whole move re-location process could probably be done in just a few short weeks, with the most timely part being disassembling the structure and transporting to the new pad. If they budget for it and build a new structure, it could only be closed for a couple of weeks while they move the floats and props.