We went last year for the 1st time in June. We usually go in Nov. Thanksgiving week. Last June we hit the worst rain that Florida had seen in previous years. They said to expect afternoon showers, but that was not what happened. They had what they called a tropical wave that just sat over them. We had torrential rain everyday, all day! It was awefull!!!! It rained so hard that the WL, where we stayed, was seeping water. My husband swore he'd never go back in June again, ever!
But with my daughter now in High School, it's hard to go any other time, so I just started planning another trip for this June. Keeping our fingers crossed that this year will be better.
Don't worry about the crowds or the afternoon rain and if your in one park and the crowds seem unbearable, go to another park. Sometimes the crowds will be lighter there.