Jim Hillestad at the Toy Soldier Museum has what looks like pizza boxes filled with the "egg crate" foam that used to come in K&C boxes back in the 90's. I bought a couple of them from him a few years back. You can safely load about 60 foot figures in them at a time, carry them where they have to go, and then reload them into the cabinets.
Kevin and I used them when we moved all my K&C down from the thrid floor out to the backyard to create big dioramas and do the natural lighting photography for the two volumes of the K&C book. We were able to move literally hundreds of figures without a hitch.
You should try to get a few of these boxes, it will make moving your collection much safer and easier.