The 777-200ER could not make IAH-SYD nonstop, even if IAH SYD is 7467nm and the 777-200ER can fly approx. 7700nm. The reason are the reserve you must count in, for example for strong head winds, and so on.
As for ETOPS 240: is it already in use? I don't think so.
dominguez(dash)online(dot)ch ... Pushing the limits of my equipment