Last week of August will be a ghost town. Why? School in Florida starts August 20th everywhere. The state made a new law that says school can't start before August 20th, so that means everyone will go back on that day. The school board kept pushing the starting date back to try and make the quarters have the same number of days. They didn't care that summer break was being pushed into spring time. So the governor stepped in and said no more, you have to start after August 20th.
June will have moderate crowds, but if you could take the kids out of school that last week of August, you'd have an empty park to yourself in the mornings.
July 4th thru August are the busy time of the summer season, that's when the parks stay open until 10pm.