As a kid, we pretty much only went the week before or after Easter, so honestly (and sadly) when I think of Disney, this is the kind of crowds I think of. And while it is definitely crowded, I can never remember a time when I felt like there was something I missed. The lines for the popular rides are long, but Fastpasses are great.
I recommend, if you can do it and are staying on property, to get up for the early hours, then park hop pretty early in the day. If you don't get up for them, then avoid that park that day. The park with the EMH seems to get the most crowded.
Also, if you want to do any sit-down dinners, make sure to decide ahead of time where you want to go and get priority seating. ESPECIALLY with a party of 6. Otherwise, you will have to wait a really long time to get into a sit-down place at any sort of normal eating hour.
My fiance and I are going the week before Easter. We sat down and looked at which parks were open early what days, and since we're not early risers, we avoided them. We gave ourselves a rough schedule of what park we're going to when, and then picked restaurants near/in those parks for those days and got priority seating. That's all the planning we're doing, and I'm not worried about it.
Be prepared to wait in line, but it's still a great time
