IMO and IME, moving the fish twice will only stress them more. I'd mostly drain the tank and put the fish into a fish-safe bucket with a lid, and take as much of the old water with you as possible.
Once you get there, set up the tank and fill it with mostly old water, and top off with dechlorinated new water, then add the fish after the filter has had a chance to clear up the water a little. if you can keep the filter media submerged, it should keep the helpful bacteria alive.
anyway once the temp is stable and everything's running, acclimate and add the fish, then do 10% water changes daily or every other day for a while to get them acclimated to the new water conditions.
HTH and good luck with the move. get it done as fast as possible, but don't worry too much about rushing. take your time and don't break anything. the fish should be fine for all day in a fish-safe 5 gal bucket.