I just went through this process with 5 cats, so I can tell you there are no easy answers. I started packing about a month before hand (I have ALOT of stuff). This gave the cats time to get used to it, play in the boxes, and also on the "new cat gymnasium" (i.e. the stacked boxes). On the day of the move I had almost all the cats in their carriers before the movers arrived. (Although one of the movers did try and pack a couple of the softsided carriers in the clothes boxes ) I went over to the house before the movers arrived and put the cats in the basement (it is a walk out basement) with their litter boxes, food, and water. This way the movers only had to deal with the guys a couple of times as they brought stuff downstairs. It basically worked out okay and all the cats were out of the way.

Good luck with the move!