OK465: But the OP also said:
my one and only goal is to stay in the air as long as possible
so although your neat solution meets the constraints, it doesn't meet the goal. I think the goal has to be met within the constraints!
Hawk: I'm struggling a bit with the idea that min drag may not be the optimum speed for maximum endurance. Min Drag = Min Thrust. Assuming constant altitude, are there situations where a jet engine can produce more thrust whilst burning fuel at a lower rate? It's only the absolute rate at which fuel is consumed that is important here, not the efficiency with which it is consumed.