Mass Move Of Servers Between Two Data Centers

Has anyone pulled off a mass server move during the middle of the night? We have decided 350 E Cermak is where we want to be but are still working out the details of where we want to be in the building.

While the final details are being finished, I need to come up with some kind of plan to pull the move off with the least amount of downtime. Our current dc is about 4 miles away from 350 Cermak and we have approximately 50 servers to move. I plan on leaving a linux box around to redirect any traffic that is ignoring TTLs.

I was thinking the best thing to do would be label and remove all harddrives, then see if a moving company could put the servers on palettes, wrap them, and move them to 350 E Cermak. Not sure if a moving company would work in the middle of the night or not.

Courier services are pretty much out. Anytime we have had a courier service move anything not in a massive box with padding, it gets bent or broken.