After Christmas, Easter is the busiest time of the year for the parks. Parks do close during the day due t capacity and this happens mpost days over the Easter holidays every year.
The weather is nicer than the summer as less hot and humid, but the parks will be very busy.
My parents have been in late September/October and have sid the weather is nice then.
We always have to go in school holidays so go in July and August. We have encountered one hurricane during our three holiday so far but all it meant was that we missed half a day of the parks. They closed early due to the weaher and opened one hour latr the next day. No rides were affected and all ran as normal. TBH you'd have never known about the weather by the next day.
It is extremely hot - can be 100 degrees and 100% humid, but you spend a lot of time inside, on rides or in aircon/fanned queues. So ime it is very much bearable, althought the waterparks can be hot going.
In July/August, ime, the queues are not bad at all - nothing like DLP that's for sure, fast passes are easy to get, and the parks are not heaving.
We are going again in August. DD will be 9 (she has been at 2y, 4y and 7y) and loves it. She is a roller coaster and ride fan and can't get enough of it. No days off here!
I would avoid Easter and Christmas generally.