We (DH, DW, DD-11, DS-9, DS-7) have been to WDW twice - May 29 - June 3, 2000, and June 1-8, 2002. Aside from the LARGE crowd at MK on GayDay Saturday, the crowds were pretty manageable both years.
Our schools are out earlier than many parts of the country, so we tried going our first free week in 2000. We were in MK on GayDay Saturday in 2000. It was crowded and hot and otherwise not our best day of the trip. Of course, I think that the crowds on any Saturday at MK are pretty large. I think that while GayDays increases the crowds at MK on Saturday, it also displaces other guests who, for political or practical reasons, head to the other parks. We had no problems with crowds the rest of the week. We used Early Entry daily and then when the crowds built up, parked hopped to a less crowded park.
In 2002, we decided to arrive at mid-day on GayDay Saturday and just have an out-of-park experience. When we checked in, our porter pulled me aside and asked if we were planning on going to MK that day. I told him that I was aware GayDays and we were spending the evening outside of the parks. The crowds the rest of the week were VERY manageable. We went to MK on Sunday, figuring that it might have fewer people in it, and were able to experience the entire left side of the park (Frontierland, Adventureland, some of Fantasyland - including Splash, BTMRR, POC, and HM twice each) before lunch. FastPass is a wonderful thing! We went during the Character Caravan era, so had no early entry perk. Even so, we were able to arrive at or before rope drop every day and still enjoy the parks before they got too crowded or too hot.
With many schools not out until mid June, I thiink it makes sense to get to WDW before 6/15. According to the GayDays site, this year's activities are from June 5 - 7, 2003, with the BIG day being June 7 at MK. I would suggest the second week in June this year, after the crowds of GayDay and before the full ramp up of Summer season.