when we moved the fish from Missouri to here (6 hour trip) we also made sure that we put all the filer media, and bio-wheels in a tub of tank water with the decorations. We left just enough water in the tank to keep the gravel moist. If you have big fish, it is easier to catch them using a bath towel as a net than to try to get them in a fish net and have them flopping on your floor. The fish should be either the first or last thing you move and be set up as soon as you get there, minimizing the time they are in the tubs (and by first thing, I mean if you make a special trip, not to pack them up and then load the moving truck). Good luck with the move, HTH.
Also, I had read somewhere before we moved the fish to throw in a handful of gravel into each tub, not sure if that is necessary if you have a sponge filter already running, but I would imagine that would be to help include some kind of bio-filtration in your tubs.