Depending on the distance you need to move. That determines different options.
Short distance, one day move. I prefer to use multiple of the same type of containers. I do not use cooler boxes at all. Put rocks into the containers, ensure they are extremely stable. Put corals and fish with the rock in same containers.
This will prevent a lot of temperature differences. Do not put any container in the sun.
Last bit of water with substrate you can leave in the tank. No need to dig all the substrate out, depending on the depth and weight of that wet sand. If a thin layer, just leave it. If deep layer, you would have to take some pout to lessen the weight.
Move the display on top of the stand if you can. Have about 10 to 20% extra water available at the other side to top up. You will waste and mess some.
Get a lot of friends together. And buy beer and pizza.
I moved my 3.2m tank with the help of my brother, son and 7 laborers. Problem with laborers from the side of the road is that they do not always understand what you want to do.