Thanks to Ron Miller (firstname.lastname@example.org) for contributing this section.[Note: No liability is assumed by the author. This is for academic interest only. If you're going to play with heavy stuff, be very careful and don't make any mistakes or you'll get hurt.]
Boxes are rather straightforward to lift from the chassis with readily available rental equipment.
Go to your local rental equipment store and ask to see their "Camper Jacks". What you're looking for is an arrangement where a length of angle-iron is attached to a fitting that slides vertically up and down a support mast. The fitting has a hand winch on it and a strap goes from the hand winch, up and over the mast and down to the angle iron. The winch and iron are actually welded or bolted together and the mast runs thru them. The mast steps into some sort of feet (T shaped). The angle iron hooks under the rail of the box and is the lifting support.
Dismount the spare tire and unhook any box-connected wiring. This may mean disconnecting tail lights (because they might be mounted on the chain boxes) and battery charging harnesses and more.
Find solid, level ground, position the jacks on either side of the box and raise the angle iron rail to the right height. Now, judge for yourself where the balance point of the box will be. We assumed that it would be centered between the lifting bolts but this might not be correct due to equipment or furniture inside the box.
Undo all the frame bolts. Remove the easy to reach bolts if you wish. At least remove the nuts. In some locations there are 2 bolts and they may be hard to see. (19mm wrenches. Might want long extensions, long breaker bar and a box wrench)
Raise the camper jacks to lift the box a bit. Verify that all the bolts are free by lifting a turn or two on the winch at a time then inspect the attach points to see what's happening. It's easy to overlook a bolt.
Expect that the rear of the box will be last to clear because the chassis will rise with it as the load is removed by the jacks. When the rear pads are slightly clear, test whether you got the thing balanced properly or not. When you've got what you want, raise the box further. It will take a pretty high lift to get the box cross-member to clear the rear shock towers.
When you're sure everything is clear roll the truck out from underneath. Now you've got the box balanced on the jacks.
We saw fit to lower the box several feet in order to rest either end lightly on some blocks in order to have 4 point stability while working on the box.
To reinstall - reverse the process paying special attention to the support nearest the gas tanks. It tends to want to come down on the tank rather than narrowly clearing it. 3 people work very well, one on each side to operate the winch, one to control direction and height and watch for obstructions (don't set it down on wires, for example).
NEVER STICK FINGERS THRU THE HOLES TO CHECK ALIGNMENT!!!!! USE ALIGNMENT PINS OR A BOLT OR JUST LOOK. NEVER, NEVER, NEVER FEEL FOR IT.