We try to be at the gates no later than 20 minutes before EMH opening time. We only did EMH once during our last visit and it was at MGM. The gates opened around 7:40 but there is a rope blocking off the attraction areas. This was the same for us when we went to MK during EE during prior visits.
We have visited EPCOT during EE on prior visits and we always arrived more than 20 minutes prior to EE opening and the gates were already open and people were in the park; we went straight to Test Track. I don't know if this is still typical for EPCOT.
If you get to MGM gates before the open and there are long lines, don't get in the middle. There are two entry gates on the far right when facing the entrance which initially have the tall iron gate blocking them so that they appear as though they won't be used. When we were there, the iron gate was rolled back about 5 minutes before the CM's started letting guests enter. No one was in line behind those entry gates except for me until the iron gate was rolled back, then a bunch of people shifted over into those two lines. We also arrived another time and got in the line on the far left. Because of the ropes in place, the line on the far left actually ended up feeding 3 or 4 entry gates, so that line moved very fast.