Hmmm, lets see.
FL410, and flight time remaining is three hours.
Not likely to be a long overwater flight where the departure weight was heavy, sounds more like a shorter sector, with suitable diversion alternates.
If it were me, descend to FL250, have the walk-around bottle available for the Commander, and divert as necessary.
FL310 would be out of the question, from my perspective.
Better safe than sorry.