The coral beauity I have is rather shy and I can only imagen that yours has become agressive due to the overcrowded nature of your tank. Unless all those fish are extramly small (like 1" in size) then your tank is to small for what you got in my view.
In fact once you put everything in a 55 you will probably have a fair amount of fish.
If your getting a new tank and you dont intend to run two tanks then its realitivly simple. Mix up 30 gal
of fresh saltwater ahead of time in a trashcan or something. Then move everything from the 20 into the 55 or 40 and then add the new saltwater to it till its full. If you move everything over then there will be no noticable cycle.
If you intend on using both tanks at the same time then put a few cups of substrate from your old tank into the new tank once its setup along with a few rocks. THis will 'seed' the new tank with bactera from the old making a cycle much faster.