I would second sending someone ahead to the gate, and having the rest meet you there. If they know that you are on the ground and on your way to the gate, they will likely not close the door on you!

Moving walkways are your friend. Use them to get to the center of the A terminal, and then again to get through the tunnel to the C concourse. Also, when you get to the escalators to the tunnel, try to pick the one with the least traffic on it so that you can walk down/up them and won't get stuck behind the masses.

Also, if possible, get seats as far towards the front of the 1st flight as possible, and politely ask the FA on that flight whether they'd be able to sneak you up near the front to get off as soon as possible (for your runner).