I think your on the right track. If the queen is in the brood box, the rest of the bees should go into the brood box. I would add the second box if you think there's not enough room for all of the bees in one. Constricting the bees too much can trigger swarming.
I wouldn't look for the queen, only evidence in 3 days time. Look for new eggs or emergency queen cells.
You can crush & strain the bucket load of honey.
Make sure you leave a bee space right around all of the frames to prevent beetles laying eggs. Keep the floor free of debris for the same reason.