You may need to search a little for a LFS that will bag and ship for you. Luckily there is one a couple of hrs from where I live that ships on a regular basis. It's not cheap, but they add O2 to the bags, place in stirofoam cooler, and add a heat source. I'm sure if you call around you will find one that will be willing to do this. I've even heard of some that will hold the fish until you are ready for them. Good luck with your search, and your move.
You could also check out the local bait shops for containers to keep your fish in while you move. I fish on a regular basis and there are several inexpensive live bait holders that would do the job for you. You can buy a transformer that will plug into a cig lighter adapter and convert your car power to 110. Then you can plug in air pump, and heater/chiller. Any computer store or office supply store will have these adapters.