I would use both filters for the first few weeks, considering that one is probably cycled, and the other one isn't, it'll speed up the cycle in the larger tank
Who knows, in the end maybe you'll be using both filters at the same time anyway? It's definitely a good idea to do so since goldfish need a lot of filtration.
But it would be such a waste of time to pour in a little bit of water at a time to those fish in the floating containers, a fish needs hours to adjust to new water, so letting them sit in a half old-half new mix for half an hour doesn't make a difference. Just make sure the temperatures are equal in the two tanks, and just let the fish in there carefully, one by one. If you notice the temperatures being drastically different in the tanks, you could tape the corners on the outside of a normal plastic bag (to make them rounder and make sure no fish will get stuck in them) and just float them in there until the temperatures are the same.
I had a little bit of old dirty tank water added to my new tank just to speed up the cycle (Adding a little waste) then letting it stand for a few days before I moved the fish. If you have gravel in the old tank, you could move that to the new one as well, the goldfish will survive two-three days without gravel before moving to the new one
Test the water every day for the first two weeks or until the ammonia disappears. You'll want to see some ammonia at the start, then it should gradually disappear and be replaced by nitrites which will later be replaced by nitrates, which are largely harmful to fish and is coped with by performing regular water changes, in that size of tank, I'd do weekly 50% changes.
During the cycle, add some beneficial bacteria to the tank after every water change, change 30-50% if you notice the ammonia rising above safe levels and DO NOT FEED YOUR FISH MORE THAN ONCE EVERY OTHER DAY
during this period.
The goldies should naturally be a little bit stressed, so it's important that you give them some plants and other hiding places in the new tank. It may be a good idea to keep the light off for the first 24 hours as well and don't feed them at all during the first day, they'll probably not want to eat.