I moved about a month ago. 4 tanks, 2 SW and 2 FW. Decided to change from a cc substrate to a DSB while I was at it. Also combined a couple of FW tanks at the same time. (Originally had 7 tanks). As far as the SW went, I took all the LR and put it in a cooler with just enough water to cover the rock. Took it to the new place and put a powerhead in there. The fish were taken in separate containers along with shrimp, snails, brittlestar. All the small fish and inverts were put into the cooler and left there overnight while the sand settled in the tanks. The lionfish had been moved two days before everything else and he was put in a bare 20g with the filter pad from the original tank and a heater . I also took several large clean containers with water from the original tanks to add to the 20g and to the main tanks.
Be careful when moving tanks that they are supported properly. If they are older tanks, watch them carefully for a few days after set up to make sure they don't spring a leak.
I will wish you luck on this. I didn't have much luck when I moved, the 55g (old tank) sprung a leak after the move, so did the 20g (another older tank that started leaking a week afterwards so it was fully stocked, gee thanks), a 40g was dropped, a 10g was smashed, and the all glass hood for the 55 was dropped as were some lights. The heater failed in the lion's tank and the water temp dropped to 68 degrees! (Thermostat in the new house failed too!) Despite all this, all the fish and inverts survived!