Alrighty Then Petty!!!
After some second thoughts I wanted to give your thoughtful argument the attention it deserved, and analyse the Tolkien quote in greater context. I found a more sizable chunk of letter 246 and also relevant sections of letter 181 (I don't personally own Humphrey Carpenter's collection of Tolkien letters and it's been a number of years since I read it).
At this point it's worth noting the Theological views of Tolkien because as a Roman Catholic he clearly was no "Calvinist"

. Much like his Anglican friend CS Lewis, he believed that Mankind (and by extension Hobbitkind) had Free Will. Most Calvinist Theologians (at least the ones at Narniaweb

) gently mock this view with the term "Free Willie", because their view essentially deprives Mankind of any REAL Free Will. God not only knows all that will be, but ACTIVELY Predestines all that will be.
Catholics and Anglicans (for the most part) see God as stepping back and allowing Sentient beings to Choose whether or not to follow His Plan. This is particularly relevant, because it means that for "Calvinist" Protestants Providence is so ubiquitous as to be nearly meaningless (EVERYTHING is God's Will); and that for Catholics, Providence works in a more subtle manner.
In their case, Providence is still God's Will (which is the Highest), but it acts "situationally". In other words, one can choose to act against God's Will or for a path that [i:3ei8gzmq][b:3ei8gzmq]coincides[/b:3ei8gzmq][/i:3ei8gzmq] with God's Will. And only when one's Own Will is depleted is Providence at Full Strength.
[quote:3ei8gzmq] [b:3ei8gzmq]letter 246:[/b:3ei8gzmq]
"[u:3ei8gzmq]At the last moment the pressure of the Ring would reach its maximum -- impossible, I should have said, for any one to resist[/u:3ei8gzmq], certainly after long possession, months of increasing torment, and when starved and exhausted. [b:3ei8gzmq]Frodo had done what he could and spent himself completely (as an instrument of Providence)[/b:3ei8gzmq] and had produced a situation in which the object of his quest could be achieved. His humility (with which he began) and his sufferings were justly rewarded by the highest honor; and his exercise of patience and mercy towards Gollum gained him Mercy: his failure was redressed."[/quote:3ei8gzmq]
[quote:3ei8gzmq][b:3ei8gzmq]letter 181:[/b:3ei8gzmq]
Frodo was in such a position: an apparently complete trap: [u:3ei8gzmq]a person of greater native power could probably never have resisted the Ring's lure to power so long; a person of less power could not hope to resist it in the final decision[/u:3ei8gzmq]. (Already Frodo had been unwilling to hard (sic) the Ring before he set out, and was incapable of surrendering it to Sam.)
The Quest . . . was bound to fail as a piece of world-plan, and also was bound to end in disaster as the story of humble Frodo's development to the 'noble', his sanctification. Fail it would and did as far as Frodo considered alone was concerned. He 'apostatized' -- and I have had one savage letter, crying out that he should have been executed as a traitor, not honoured. . . .
[/quote:3ei8gzmq]
Thus, the moment Frodo's Will was completely subsumed by The Ring, he ceased to be an Active Agent of Providence. His Will (as was Gollum's) was at that point "utterly spent". He had completed his Quest (i.e. "produced a situation"

--get the Ring to Mt Doom--and could do no more than that, no-one could (which means he is NOT a "failed Hero" as so many erroneously believe, including Frodo himself). So the only Force greater than the Ring's Will, [b:3ei8gzmq]at that point[/b:3ei8gzmq], was Eru's Will, i.e. Providence, which shifted the odds in favour of Frodo, and against the Ring and Gollum.
This is true in both Tolkien's version AND Jackson's version. As I've already pointed out, it makes no difference to Providence how long the struggle lasted, or whether Frodo attacked Gollum, because they were both controlled by the Ring, and only the Power of Providence could act against it.
In Tolkien's version, Providence alters the odds causing Gollum to fall into the pit while dancing with Glee. In Jackson's, Providence uses the protracted struggle to send both over the ledge, but allowing Frodo time to clasp the edge while Gollum continues on down with the Ring.
So I'm sorry Petty. I wanted to give your argument a fair shake. But in no way do Tolkien's comments contradict my argument.
But again, you proffered a valiant and cogent argument

, but it doesn't shake out in the context of how Providence works, or how Tolkien understood it, and how Jackson filmed it.
[b:3ei8gzmq]GB[/b:3ei8gzmq]