I know its different engines and a heavier 380 takeoff weight, but EK figures for DXB to LAX yesterday (7491nm) are TOW = 565t (max 575t) revenue carried 55.5t (full seats of 489 plus a 4.5t freight) with a wind component of 0kts (over the pole).
LAX to DXB (7522nm) TOW 575t revenue carried 58.5t (full 489 seats plus 7.5t freight).
EK always carries an ALTN.
The Don