Early morning flights sound like a good idea -- until you do the math and figure out just how early everyone needs to get up, shower, get dressed, get the bags to the DME pick-up location, and be there around 15 minutes before scheduled pick-up time. Then it doesn't sound so good.
There's a reason why there are more cheap seats on early morning flights!
Also, you can't use Resort Airline Check-in (RAC) for early morning flights because RAC doesn't open until 5:00 a.m.
If I had to fly very early in the morning because of very significant cost savings or because it was my only choice, I would check out from Disney on the day before, take DME to the airport the night before, and spend the final night before the flight at the Orlando Airport Hyatt in the terminal.