The queen will lay as long as there is pollen and nectar coming in. It takes 3 weeks for the eggs to emerge as adult bees, and a few more days for it to fly. Therefore, you must leave the cone on for a minimum of 4 weeks after the cone is "secure", or after the last hole is plugged. Then you wait a week with no bees leaving the cone. I have done them in 5 weeks, it has taken up to 10 or 11 weeks.
The catch box bees must eat. If there is a flow going on, no feed is needed. If no flow, then you need to create one. "feed"
PS. If there are any bees trying to get back in the cone, they came out within the last 3 days, whether you seen them emerge or not, so don't start your 4 day count until none are trying to return. Then only after 4 or more weeks after you plugged the last hole.
Since you are in southern Florida, I cannot say what the SHB will do inside the trapped hive.