May is not too close. But my preference is September.
Weather is unpredictable, but it is typically a little cooler at night.
Crowds are certainly lighter. We were at SSR for a week in September 07. On Labor Day I stopped by the front desk to ask a question. During the conversation the CM told me 650 guests were checking out and 27 were checking it. The next day we swam at the main pool and there were only 6-7 other guests in the pool. Pretty nice!