Last year we arrived the Sunday before Memorial Day. We did Epcot on Sunday and Monday. It was pretty packed, but manageable.
On Tuesday we went to MK at RD and got a whole lot done before the crowds piled in. The afternoon at MK was plain crazy. Lots and lots of people. The most crowded day of any of the days we were there.
On Thursday, we did AK, which happened to be the designated park for Gay Days. I do not know if that scared a lot of people off, but it was our best and least crowded day in any of the parks. Rode EE multiple times and pretty much rode and saw everything else we wanted to see before 2pm.
On Friday my son and I were up early to be at HS when it opened bright and early for Star Wars Weekends. Once again this was the designated park for Gay Days. Reading he thread for Star Wars weekends after the fact, it seemed that most felt that was the least crowded SWW dates up to that point. We probably rode Star Tours three times in a row within the first 30 minutes of being in the park. We did all the other Star Wars stuff and had a great day.
So, it will be slightly crowded that week, but I think it is manageable. If you do rope drop any day, I would do it for the MK and HS days for sure.