Wow, i am surprised to hear about the people avoiding EMHs. I go for Easter every year and never had a problem. We will be arriving on the 3rd this year. Sure, it's busy but I find Disney busy all the time now so Easter doesn't make a difference. I am not a crowd person, when it gets to where you can't move, i get weird. So if I can take Easter in the parks, anyone can. My experience is that the only really crazy day is Easter Sunday. Here are some things that I do:
1. Easter Day: You do 1 of 2 things. Go to the Magic Kingdom early. With all the activities going on at the resorts as well as it being a holiday, some people may choose not to rush out to the parks. I prefer to go and see Easter on Main Street. The southern belle girls (I keep forgetting their names, help!) are so pretty to see all lined up. and they may have a small Easter Pre-Parade before the 3pm parade, and the Easter Bunny is there too. However, after the parade, I would head out and do something else because then it will start to get busy (Maybe by noon).
You can also choose for not go to a park that day and just relax at the resort. I know you are staying off site, but some of the resorts in house have some various activities. The Grand Floridian had a beautiful Easter egg display in the lobby; that was great to see. and the Polynesian always has a candy grab. But I am not sure what they are doing this year with all the refurbs going on. They also have various characters dressed for Easter out. I met Thumper at the Poly about 2 years ago. Either way, use this day as a more relaxing, non park day and end the night with a nice dinner. We are doing the Yahtsman this year.
Good luck! and don't be afraid of the crowds, they aren't that bad, you just have to be mindful of them. Good luck!