Nice piece of work,
Alcuin.
For right now, I'm only going to respond to one little thing that you wrote.
Quote:
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In that case, the propitious fall of the Elven rope after its use is due either to “Elvish magic” or the kind of Providence that led Gildor and the wandering Noldor to come upon Frodo, Sam, and Pippin in the Woody End just in time to scare off the Nazgűl tracking them.
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If it was "Elvish magic", I think they would have been told about it (as they were told about the boats and cloaks), and I also believe that we would've seen the magic in operation in Lothlorien. Surely Haldir would've taken advantage of it.
As far as providence, which I had already considered and just not mentioned yet- why waste providence on this situation? Tolkien only uses happy chance and divine intervention when it makes sense. Why use it now? It served no purpose. It did not help them hide from Gollum in the least. He found them that very night despite the absence of the rope on the cliff. And the rope proved to be useless as a leash for Gollum, as he could not abide the touch of it. There was no need for the rope to be saved.