Well, I have moved many times with Tex, but he is an inside only cat (though we do have brief excursions, heavily supervised, to the great outdoors). I think it is best to keep everyone tightly confined for a few days, completely. Let the dust settle, and get everyone very used to their new litterboxes. Then, keep everyone under close watch for awhile. I moved two years ago with three of the herd, and I don't think it was more than a week before they felt settled. Tex did hide on th furnace for a long time, though, when he would get re-startled by something new.

Good luck!