Keep as much water as possible. If you have LR
, make sure you keep it in water in some kind of tub... same for LS
if you have it. definitely DON'T try to put it in containers larger than 5-10 gallons as it will be difficult to carry... I wouldn't risk it. Keep plenty of new saltwater there to add in.
If you can keep all or almost all the water, you can add that into your new 60 and top off with freshly made SW
... it'll be just like you did a water change. Just try not to move the fish around too much... they should be put back into the tank after the water temp and everything else is stable.
It's a pain in the @ss, but with more planning comes an easier time. You shouldn't have to deal with that big of a new cycle at all as long as you can keep the rock and other parts of your tank in water and as close to proper temp as possible. Just don't try to move the tank with any amount of water in it as it may break on ya. 8O