We are planning to go to WDW May 27-June 2.
That is a busy time regardless, however, weekdays are sure to be 'less' crowded than the weekend.
My suggestion is to be at the gates before opening and start your parks then. After lunch/evening the crowds increase even more. You will get through more rides this way.
And just some strategies we have used at Magic Kingdom.. all 3 are immediately upon the gate opening.
a. I go directly to the character pictures while DH goes straight to the back of the park to get a fast pass for peter pan or another ride we like.
b. Teens and little kids go directly to buzz lightyear while I go to back of park to get a fast pass.
c. I take DD to teacups while boys go to space mountain.
At Epcot, you would want to go directly to soaring. Sometimes there is a second rope drop so you have to wait again. We go directly to the fast pass machine and get fast passes, then go directly in line for soaring. After coming off soaring we go directly to test track and ride that. Hopefully by the time we are done we can get another fast pass for test track to ride again later.
We've gone during Memorial Day Weekend and I didn't find it to be as crowded as I expected - and that was years before we ever braved the Easter/Spring Break crowds -
Val, Co-CL Disney Vacations