LAN (Chile) flight 801 from Santiago-Auckland is 13 hours nonstop in an Airbus 343, without any sight of land in between. I don't think there are many airports suitable for a heavy jet on the way
(I'm not sure about Easter Island - it's a long way off the great circle route.)
Perth - Jo'burg (SA281) is almost as far and Kerguelen doesn't look very attractive for a diversion!