Hello,
I responded privately to share my experiences with moving map collections. I have done it twice. Map cabinets can be moved stacked, with the drawers in place if you have doors and an elevator that can accommodate them. The facilities group that moved the cases flat for me had piano/appliance moving dollies (
http://handtrucks2go.com/Twin-Dolly-Trucks-for-Pianos-and-Appliances.html) that get slipped under the load at both ends. The dollies have a built-in jack that raises the load and the wheels on the dollies swivel in various directions so that the stack can be wheeled around corners, through doors, onto elevators and into the new location.
A moving company did the collection at Arizona State. They were supposed to use inflatable balloons to keep the maps in place in the drawers when they tipped the cabinet sections onto their backs. They did not use the balloons, so the maps slipped towards the back of the cases. Luckily, all of those cases had dust covers, so the disruption was somewhat minor. We had to open each drawer and pull the maps in their folders back into their proper place.
I highly recommend the piano/appliance dollies. Your campus movers could use them for other equipment as well (file & fiche cabinets in a library). Linda Zellmer