I got my EAD today from Newark, NJ.
I reached the office at the time they wanted me to be there. I went to the window, submitted my appointment letter and was asked to wait.
After a few hours, I was called to the window again, and asked if I had the original receipt letter. After I showed it, I was asked if I had a copy of the same receipt letter and I said yes. (The appointment letter asked me to carry a copy of a lot of forms and documents.) When she saw me taking out a big bundle of copies of all document, the immigration officer was impressed and she said, "You actually followed all the instructions!, that's very good" and I just smiled back.
I was then asked to go to another room and wait. After some time, a whole bunch of people were called in along with me. They took photographs for the EAD. After 5-10 min, I was handed my EAD card.
I am not sure if going in early helps or not. When I went to get my EAD picture, my group had people who were there before me and people who came in after me.
Regards,
AmIinTrouble