Plan for heat. By mid day usually reach upper 80's. Im a very active person (12+ hours a week triathlon training consisting of riding my bike 80+ miles, running 25+ miles and swimming 3 hours) and the May heat and walking 6+ miles a day takes it's toll on me. Id suggest bringing water bottles and refilling them throughout the day rather than standing in counter service lines every time you want some water. Hydrate, hydrate, hydrate.
Although this year has been dry I'd also plan for a rain shower each day, at least in the forecast.
Eat breakfast in your room or on the go and if you are awake and in a park early in the morning be there doing attractions before the temps rise and attendance picks up. If you want to do a character meal do it for lunch or dinner when you're tired and want/need the break and the park now has longer standby lines.
Once you get into and past the third week alot of southern states are out of school and the crowds usually pick up. Lighter crowds doesn't mean you shouldn't pay attention to recommended and non recommended parks it means you should pay MORE attention to them. In July, it's crowded everywhere so it almost doesn't matter where you are at 1 pm. In early May the difference between the right park and the wrong park at 1 pm could be dramatic.