I would recommend the June dates. Our school district usually lets out the end of May, but for some reason this year, we don't get out until June 9th (also adding a couple of snow days).
If you are thinking of going Deluxe, I would recommend the Contemporary. Especially since you're going in the summer (when it's hot and crowded). It is so easy to just jump on the monorail with the kids and get to MK for the morning. Then, when it's around lunchtime and it starts getting too hot, and the crowds start coming in, you can easily head back to the resort for naps/swimming. Then in the evening, when it starts cooling off a bit (sometime after 5-6pm), you can head to a different park. We just can't seem to successfully manage doing this unless we are staying at a monorail resort. Those darn resort busses just suck up way too much time.
Oh, and we fit 6 people (one was an infant) comfortably in a room at the Contemporary.
HTH