We got to Epcot and MK 45 m inutes before opening last year and the lines were never that crazy. We were the 5th family at the turnstile or so each time and there was no pushing or anything like that. That was saved for the rope drop at Tomorrowland
At AK, it was a whole different story. We got there early, but there were a ton of Brazilian tour groups. They let everyone just wander into the park and there were Brazilian teenagers generall misbehaving everywhere you looked. That coupled with the heat factor made me never want to stop foot in AK again
Just wanted to add that we stayed offsite and driove each day to the parks.