Your plan sounds fine for you. I use all mediums so I would just fix the comb with rubber bands, move the supers, and set a leafy branch in front of the entrance so the bees will reorient when they leave the hive. Ordinarily, I would wait a few days if the swarm had just moved in in case the swarm had a virgin queen who needed to mate. But it sounds like they have been there long enough already. (You might look for eggs when you fix the comb.) I would wait until after dark to actually move the hive if it was convenient to do so. I hope it goes well for you.