You consider 7 players a big group? We have almost always had between 8-10 active players, heck, I even went for almost a year with 12 once.
The key is to keep the action going. Unless it is absolutely necessary I usually bypass the initiative rules, and just go around the table asking each player what their character is doing. I'll either do this clockwise based upon where the players are sitting, or based on where their miniatures are, depending upon what make the most sense for that situation.
I also try to make sure that the party sticks together, or if they do split up it is based upon who is present at the game, with the characters of the absent players going off on their own. I also try to cover any solo play outside of the group game, either contacting the player between games or having them arrive early the following week to run through their character actions. I do, however, allow the passing of notecards during games for solo situations as that tends to not slow the game down too much.