General thoughts:
Max endurance is a holding problem, so fly at optimum holding altitude and speed. To satisfy the constraint of of a single speed and altitude for the rest of the flight, you could use an average weight for the rest of the flight. However, fuel flow will be higher at the initial weight, so I would bias toward that. So optimum holding at 2/3 fuel of the initial condition is probably good.
Finally, I suspect for a B777 single-engine holding is a lower fuel flow than holding with both engines operating (one engine provides sufficient thrust while operating at a more efficient RPM).
I would look at optimum SE holding at 200 or 205T. Probably the altitude is in the high teens/low 20s. If you need to take the descent into account, use a SE descent at the hold speed.