No other way ?

[Legate of Amon Lanc]

Originally Posted by Rune Son of Bjarne

I personally think that there would have been other ways, but I doubt that they would have been alternatives. One could have spend ages searching for passes over the mountains and they would probably also have been guarded, but probably only by orcs.

Yeah, I think here is the answer. You have to consider the need for speed and that Frodo&co. had to know a way which would surely take them where they want, not that they find some pass and after a week of walking on the edge of exhaustion a great uncrossable fissure, or worse, an Orc tower, appears right before them. Also, remember Emyn Muil, what trouble it caused, and it was much easier terrain.
So: the passages probably have been there, but they surely could not serve good for Frodo's purposes.