I don't know where this every two hours stuff is coming from. Can't speak for the 777 but on the ER for over 12 hr legs the breaks usually go long/long or short/long/short. The crew discusses it comes up with a consensus before takeoff.
I think there should be only 1 pic, unity of command you know. The idea of splitting up the leg I think is terrible. Jmho. Also it sounds like I never want to e based in Atlanta.