How far is the move? When you move, tanks are the last to go. Probably not even done on the same day as the house stuff move. Don't take the substrate out not even the plants. Catch fish, drain, move, fill, add fish. Drive to the new house so that the gravel doesn't move around. I think you complicated this with the 20 gal consolidation. When you move a twenty it's so easy. If the fish are small, and you can drive to keep it from moving around too much, you can literally leave the guppies in an inch of water in the tank while you go across town. It's most important that your canister media have access to oxygen during the move so if it's in an open top cooler you wouldn't really need an air-stone. It wouldn't hurt, but if it's a short drive it's going to be back up and running asap right? You need a couple buckets of dechlorinated water to do any rinsing of bio media. Don't use tap water on your bacteria in other words.