Okay, I'm going to take a guess.
First week of June should be okay. I understand the summer is crazy and the weather is HOT and HUMID!!!
Late August through September there will probably be Free Dining packages offered. This increases the crowds where there used to be a slow period. Still not bad, and your group could maybe get a free dining package and/or a room-only code (they are usually released for this time period as well).
Late September the weather begins to moderate a bit and then the Wine and Harvest Festival begins late September as well.
Downside is that it is Hurricane season, so anything is possible.
Very early June and/or late August if you need to go June/July/August .... otherwise, I would suggest mid- to late-September because of the offers, weather, etc.