Simple answer; try not to make any other plans on move day except moving.
This day is considered to be one of the most stressful things people do. It s best not to add to this if possible.
If you can, move the day before you need to be out of your current home, and then have that day free to do your cleaning and last minute arrangements.
If there is no way around it and you have to clean move day, ask your moving company at time of booking approx. what time they will be finished loading at your current home.