Coolers are a great way to transport large fish. You can also use the cheap styrofoam ones, if you use large fish bags to line them.
Break down the tank at the last possible time, and load that in last, so it is first out at the destination. Load the fish in coolers, buckets. Home Depot buckets with lids are a great option.
Fishing supply stores should have battery operated air pumps which will help keep water aerated.
Several brands of ammonia neutralizer are available, can use that to help reduce stress .
Some people ship Fish with methylene blue, which helps with oxygenation, but the air pump is a better idea.
Use an extra bucket to keep filter media damp or wet, to preserve bacteria
Upon arrival , get tank into place first thing. Have all equipment packed up and easily available. Ensure you have enough water conditioner available. If you can, sort out where you will get the water from at the new home, I.e bucket brigade, hose from sink, hose from hose Bibb outside, etc, and have the parts/pieces available to fill tank. Get tank filled, and start acclimating Fish, get filters installed.
I have moved large Fish ( oscars, Jaguars, dovii, Vieja species, )from Illinois to Missouri this way.
