To have a hope of putting it together again you must code everything and document everything.
Give every cabinet a number or letter code.
Give every connector or terminal a number or letter code, maybe its cabinet code, plus a letter for left or right and a number from top to bottom. So every wire or cable has a tag showing what terminal or connector it goes with. (Maybe some wires and terminals have IBM original coding, then of course use that, but it will help later if you know, this cable comes out of cabinet C and terminates on the left bottom of cabinet D.)
Go into the place before moving day, with a good flashlight and a laptop and a camera and spend a few hours just working out this system.
When you begin to take things apart, go slowly and take many many pictures. Maybe you can designate one person the official photographer? You will be busy supervising.
On moving day do not forget to bring extra camera batteries, SD cards, camera battery charger!
Above all, please please PLEASE! do not deface the objects with adhesive tape or permanent marker or any kind of adhesive label!
I have documented many artifacts at the Computer History Museum that came from the collections of hopeful amateurs, and so many times I must record: "adhesive residue" -- "deteriorated masking tape stuck to object" -- "large number in permanent marker". These make permanent damage that can never be cleaned up. There was a collection from Germany, the amateur owner stuck a big A4-size label on every object with some kind of glue. Those labels will be there forever because getting them off might cause worse damage.
Here are some tags that work well:
Use tags like that to code your cable-ends and terminals -- not markers or adhesive labels!
It is probably hopeless to ask, but it would be good if everyone who handles the machines wears gloves. Not so important handling painted surfaces but when handling plastic, or bare metal, human finger oil can leave permanent marks. At least have a supply of gloves like this:
http://www.universityproducts.com/cart.php?m=product_list&c=667for your crew to use.
Maybe you cannot afford to pay professional movers? But maybe you can go to a professional moving company and rent 3-4 dozen blankets like that. You wrap each cabinet in blankets. It is OK to use lots of masking tape to hold the blankets in place, if the tape is on the blanket, not the machine!
You can use this to wrap anything like a mummy. You can go around and around a cabinet with it to make sure the doors will not swing open. Then you put the blankets on, and go around and around again to hold the blankets in place. You can wrap it around a bunch of cables to hold them against the side of a cabinet so they don't dangle.
Best of luck with this!