The last week of August works for us. I chose not to pull the kids out of school for a vacation, or atleast one that will be ten days or more. The last week of August is usually not crowded but it is hot/humid. The rain usually is a minimal shower in the afternoon, we call them the 3:00 showers. For us the humidity is no worse than being in Philly and if you pace yourself and take a break for a swim it works.
In 2002 we changed it up a bit and went in June. NEVER AGAIN. I thought it was much more crowded and the fact that, although it was a stoke of bad luck, it poured and I mean torrential downpours for the whole week. My feet were permanently shriveled for the whole week.
I think the fact that schools in the south go back to school early cuts down on attendance and the lines usually aren't more than 20 minutes for the "E" ticket attractions.
Once the kids are off to college and it's just hubby and I, I'd like to go during Nov-Dec. Been there in early November and thought it was just beautiful but that was about 20 years ago before the kiddos were born.