We were there the over the Easter Weekend and the week after in 2002.
The waterparks were closed each day by 11:00 due to filling to capacity. Same for MGM & MK. We never made it to a water park.
As long as you get up early and be at the parks well before opening, you'll be able to do most of what you want to do by noon, then head back & relax at the pool & your resort for the afternoon (trust me on that one).
The crowds did NOT let up later in the week. In fact, the MK became so frighteningly crowded by noon on Wednesday of that week that I feared for my DW & DD's safety. Seriously.
Epcot was not quite as crowded, in fact the afternoon seemed like a pretty good time to do future World (except, of course, for TT). Mission Space should change some of the crowd dynamics.
Having said all that, we had a wonderful time, because we planned with the help of these boards and the Unofficial Guide. We enjoyed the week thouroughly. Bottom line: if you sleep in, be prepared to deal with unimaginably large crowds, or even the potential of being shut out of the MK, MGM, or definitely the water parks. Above all, have fun!