We go to morning EMH almost every day of our trips.
We also go during the end of May (Memorial Day) and are able to walk on to most attractions during that first hour. We are able to see most of a park and we head back to the resort for a nap just as the crowds/lines are starting to form (around 11:00). Later in the day, the major attractions can have 2 hour waits.
The kids and I are not morning people, but it's worth it for us. We bathe and set out clothes the night before, so we just have to brush teeth and hair and we're ready to go. We keep breakfast foods in the room, so we can just eat something on the way to the bus stop. We get as much done in the morning as possible and then take a nap for several hours. We return to a park for the evening, but usually relax and take a slower pace.
We go to several evening EMHs (we always get park hoppers), but have found that there still tend to be long lines at that time of year.