We have never done an early EMH. Matter of fact, the two times we did PPO at BOG for breakfast, while it was fun, by noon we were wiped out & went back for a nap or rest.
I don't like to have to get up & out early on vacation, and neither does me DD (she & I go most often together). I like to have my coffee and relax, then we're likely at a park about lunch time.
Evening ones are okay - but if we do that, we'll likely get a later start or take a break in the afternoon.
We're almost never at a park before lunchtime! We get up by 5am most weekdays, so vacation to her is sleeping in, having a muffin and coffee and relaxing until either of us feels like getting going.
Late night at the MK, it seems most little kids are in bed, so the wait times and crowds are much lower.