I don't think you're overthinking it at all. I would try to save as much water from the old tank as possible, only to minimiuze any chemical differences between the old tank and the new. I'd use a powerhead in the tub with the LR
to keep some circulation and maybe an airstone in the bucket with the fish. What kind of fish do you have and how large? It might be a good investment to pick up a "muck bucket" from Home Depot to give the fish some more room while you're moving things over. They cost about $6 and will get you about 15 gallons of water and a LOT more surfacec area to promote gas exchange.
Word of advice though, DON'T try to pick one up full of water by the handles. Last time I did, the handle broke and I ended up with about 10 gallons of freshly made saltwater all over my floor. I now place it at my tank and fill it with a 5 gallon bucket to pump water back to the tank. Also, double check the point where the plastic went into the mold. I had a new one crack right there at the "button" leaking my RO
water once. (Actually, the same day as the handle breaking on an old one. One heckuva day!) I chalk it up to bad luck, but other than thoise two events, I've been using these for years with no other failures for mixing water or transporting live rock when I move.