We're in the same boat so I'm interested in what people say as well. We were considering mid June, especially since our kids are out on the 8th this year which is almost "early" June. However, with 2 boys in travel soccer, this would miss 2 weeks right in the middle of their seasons, and I'm certain one of them (if not both) would miss a tournament. Since we were renting a house and it was already booked one of those weeks, we decided to avoid soccer season altogether and we're going July 28 - August 11, which gets us back one day before two-a-days for High School soccer start.
I've seen a zillion threads saying that the end of August is the best time to go in the summer, but that's not possible for us so I'm hoping early August will still be okay. We're staying 2 weeks and spending 10 days at Disney. We're also hoping that if we get to the parks before opening on those 10 mornings (9am since we'll be offsite) and stay until 1 or so (obviously at non-EMH parks), that we'll be ahead of the crowds, even if we can't avoid them totally. We're planning afternoons for relaxing at the house/pool, and evenings for golf or waterparks (after the thunderstorms and before dark and/or closing so 5-7pm or so) or just exploring the parks a bit and doing those things we never get a chance to (all the areas at the end of the big rides at Epcot, pin trading, Innoventions, shops, nature trails, etc.). From what I've read for the summer, the lines will still be pretty bad in the evenings so we're not targeting that time for rides.