We were also there the last week of April '05 and our best strategy was to hit the parks at opening and ride as many rides as we could before the huge crowds hit. We avoided all the EMH parks other than our last day when we made the mistake of going to the early EMH at Magic Kingdom. It was INSANELY busy. The Magic Kingdom and Animal Kingdom were both packed by lunchtime so we left and took a break at our resort. MK was then much more manageable after about 5pm. Our kids were 4 and 2 so we never stayed much later than 8pm, but we had a WONDERFUL trip and rode/saw just about everything we wanted at all 4 parks in 6 days. Plan, BE FLEXIBLE and know what to expect and you will have an excellent time!!!
Also, WDW was much busier than usual for the last week of April last year because Passover fell at that time and many Eastern schools including NYC public schools had their spring break that week.