Rock Flower Anemones are very hardy. I collect the shallow water less colorful variety when I snorkel in the Florida Keys. The colorful ones come from 30 to 50 feet deep and I'm just snorkeling, not scuba diving.
Anyway, I collect them and put them in a cooler full of ocean water and a bubbler in our Zodiac. They get back to our motel and get transferred to another tank with ocean water, a bubbler and a powerhead. That water gets a 50% to 90% water change every day for the 2 or 3 days we are there in the Keys. Then they get put in our car with just a bubbler for the 5 hour drive home. There they get transferred to a 5, 10 or 20 gallon holding tank with water I make using IO Reef Crystals. They stay in the holding tank for 2 to 10 days and then get moved to either my 90g DT or my 16g RFA breeding tank.
If they can go through all that and survive (99% survive), I think you can move your RFAs at the same time you move your corals. Maybe even before your corals so they get to settle in and won't move around and damage any corals.
Are your RFAs already attached to rocks that you will move to the new tank?