We did it on a non EMH day last month and it went great, better than I expected. A friend followed what we did this week and it worked great for them too.
Are you staying within walking distance, or are you driving in? What we did since were were walking from the hotel is that DH went over at 7:00 a.m. (the park opened at 8:00). He went to either gate 14 or 19 as those have trees in front of them, so are often the last to have someone line up in front of them. He wound up being first in line at that gate. DD and I got there about 7:30. We were going to just get in line and meet him inside, but his line wasn't that long yet, and the people in it told us just to go up with him, so we did. If you are all going together- I would suggest being there an hour before the park opens, especially with the park opening a little later now.
Then once they opened the gates, DH booked it with the other Dads and a couple of jogger moms down to the castle/hub- left side, and DD and I followed at a fast walk. That is where they do rope drop. There was no designated A&E line on our day- and a CM specifically came out and told us that there would not be. If there is no designated line your day, the rope drops from your right side, so that is where you want to be to get to the front of the pack. For us, once the rope dropped, DH took off with the other Dads and DD and I did a fast walk. DH could have been first in line, but he let some Dads pass him since he knew DD and I were not running. DD and I actually would not have been horribly far back even without DH running ahead and getting a spot. We wound up letting people go ahead of us for a while because our day, it started with just Anna, no Elsa, and we wanted to see both and didn't want to have to do it twice. Sometimes they are both there at the start (the day before we were there), sometimes it is 30 minutes before the missing one joins, and sometimes it is an hour. Our day was an hour, but it was still worth not missing more park time than that. The line was consistently 2 hours or more when we looked during our trip.
This week when my friend did it- there was a designated line from the hub area. When the gates opened, they walked to the hub/castle area. Because they did not run and there were several runners and faster walkers their day, they wound up quite a ways back in the line, but still not horrible. They were led down to the meet and greet area. Both Anna and Elsa were there from the start (she said she heard only Elsa had been there at opening the day before). Even being further back in line, they were done within an hour. She also reported that the lines seemed to be 2 to 3 hours the rest of the day.
Good luck! Hope it goes well for you!