Looks like we can only go in summer again. Last year went for first time in late August. Very hot of course, but not crowded. Got lucky in between the Hurricanes. Is there much of a difference between late August and mid-June as far as weather and crowds?
Usually the humidity isn't quite as bad until August. Also be prepared for afternoon rain, every day. A quick 15-20 minute rainshower is a regular occurence all summer.