77L could do BRS-DXB comfortably... I assume ground handling at BRS is satisfactory for a 200LR? Even the 77W could do it with minimal payload restrictions but (and I may be wrong) BRS seems a bit tight for anything that size.
If not EK, QR could certainly do DOH with the 788 or EY to AUH with the 789. Although I think EK has the better odds.