It has nothing to do with automatic or manual transmissin. when you climb at high altitude, the air gets cold and thin. the engine doesn't get required air combustion slows down and vehicle starts under performing.
your suggestion for 4x4 is logical. you may need 4x4 once in a whole trip and if you dont have, you may be stucked for a long time.
another important tip: always travel in a group of two or three vehicles in such lonely areas. in case of a breakdown, your companion can pull you to the safe place.
at the end, I must say your driving skills are excellent. atleast I cant even think of driving a car to these trains. But its always man behind the gun (in this case behind the wheel).
