[Formendacil]

If "The Passage of the Marshes" was a travel chapter, "The Black Gate is Closed" is the opposite: a chapter taking place mostly in a single spot, usually for a shorter duration of time.

This is the point in the book where Gandalf's plan for the journey that started in Rivendell comes to its last gasp. The ways and means were always a bit murky after Lorien, but the overall plan held as far as reaching Mordor. There isn't even a clue how to get in, though. Hence the fact that the meat of this chapter is in Gollum's revelation of another way, and hence a bulk of this thread is spent on discussing how else Frodo might have crossed into Mordor.

For myself, I think it plain that Gandalf did not mean to take either the Morannon or Cirith Ungol, nor the very long road east to the "back door," nor to use the eagles (the circling Nazgul here should be a reminder for book fans just what a poor idea that would be--the eagles can't get involved until the Ring has already slipped right up to Orodruin). Does this leave any options?

I think (similar, I hope, to what 2005-me meant all those years ago) that we simply don't have enough information to say that both the Ephel Duath and the Ered Lithui were COMPLETELY insurmountable. Crossing them without guide or equipment, though would as like have been deadly for Frodo and Sam as the Morannon, especially on their limited rations. I incline to think the Ered Lithui more likely: crossing it closer to Mount Doom saves them a lot of the way across Gorgoroth and since it faces the empty plains of Rhovannion rather than Sauron's archenemies in Gondor, it seems to have an advantage on the Ephel Duath-Gollum's assertion that Cirith Ungol is better than the Morannon because Sauron can't watch everywhere seems to be borne out by events.