Coming from a tilers point of view, it depends on what kind of tile they are doing depending on if he could move the tank out and then move it back in within just a few hours. even if they are doing sticky tile he already said they have carpet down so they will have to pull that up, clean the floor, paint the floor with a primer, and then place the tile down. This very easily could take two to three days.
I would say empty the tank to the lowest possable water level, move the tank out of the room even if into the hallway or right outside your room. Is there any way of waiting to do a water change to move the tank out, and then letting it set in the "new location" until it needs another water change? (remove the water in the room, move the tank, then replace the water, then when time to do another remove water, move tank, replace water)
As long as you can lift the stand and the tank that has a minimun about of water in you should be ok. Just don't try lifting a tank with water in it and nothing underneith, or you will end up with a new Neat-o WET tile floor