| Welcome Striped!
You don't really need to go that technical with it. 4 weeks should be a sufficient ammount of time for the cycle to progress normally. Set up the new tank, and just run the old filter on it for the first two weeks then switch over to the new one. By this time the cycle will have begun. Let it run until you test no Ammonia and no Nitrite.
There is no need to transfer any of the old water over to the new tank as the bacteria don't really swim through the water column, they colonize porus substrate and filter media staying on the surface.
You can help 'seed' the bacteria into the new tank by transferring some of the gravel from the old tank to the new. Anywhere from 25-50% of the old gravel will help to speed the colonization of the bacteria throughout the new substrate. Mix the old gravel in clumps all around the tank roughly covering the entire bottom and try to bury a few pockets all the way down to the bottom of the new gravel so that it helps populate the lower regions of the bed.
Cichlids and Oscars both produce a lot of waste being carnivores and you should make regular water changes around 20-25% if you feed them often. But they are both pretty hardy fish and can rough it out if necessary and if they have been kept healthy up to this point. Even still I would take the earlier advice and leave them in the 20 gallon until the tank is fully cycled.
__________________ "The only thing that happens fast in saltwater tanks is failure."
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