I suspect there's one critical problem.
I don't think anyone could throw the ring in.
It's conjecture on my part, but here's the idea:
We know for sure there was a spell on the ring that made people not want to hurt it (we see it as early as the fireplace scene, where Gandalf tells Frodo to toss it in). We also know for sure that Sauron and the Ring's magic gets much stronger closer to Mt. Doom.
Based on these two things, I think once you get to "Sammath Naur" (the forge in Mt Doom), it's so strong that nobody, no matter who they are, could resist it — at least not if they're the bearer. We'll never know if a few unbelievably strong-willed characters like Gandalf could overcome that, but I think the fear that both Gandalf and Galadriel expressed about the ring getting power over their will, if they took it (and they'd have to take it, to do this), suggests that they too wouldn't be able to resist it.
Frodo and Isildur were the two working examples, and they both came off as very stoic, strong-willed "good people" — but they totally crumbled in there. Between that and the fear on Gandalf/Galadriel's part, I don't think anyone could resist it.
I think that — in deliberate irony, all of Sauron's spells essentially worked as designed, and he was "hoist by his own petard".
It was actually impossible for anyone to walk in there and throw in the ring. The only thing that made it possible... was Sauron's own magic — specifically, his choice of wanting the ring's power to be one of command and enslavement.
There's a very strange thing that I picked up on in the books where - as far as I can tell, Frodo actually uses some of the "higher" powers of the ring on gollum - he actually uses it's power of command, telling him to throw himself in if he dares to try to take the ring. At first I was a little doubtful of this interpretation, but Tolkien actually repeats this in multiple scenes in the second half of the tale, to the point where I think he was repeating himself so it wouldn't get misinterpreted.
That "command" works. Sauron's own "make a ring that lets you command others" is the very thing that gets through his indomitable "don't you dare hurt the ring" spell. It feels right to me that Tolkien would have wanted Sauron's own evil — the evil of mental enslavement, to be the very thing that would destroy him in the end.
It starts with the promise he made, when they run into him right after Frodo and Sam cross the river:
'Sméagol,' said Gollum suddenly and clearly, opening his eyes wide and staring at Frodo with a strange light. 'Sméagol will swear on the Precious.'
Frodo drew himself up, and again Sam was startled by his words and his stern voice. 'On the Precious? How dare you? ' he said. 'Think!
One Ring to rule them all and in the Darkness bind them.
Would you commit your promise to that, Sméagol? It will hold you. But it is more treacherous than you are. It may twist your words. Beware!'
Gollum cowered. 'On the Precious. on the Precious! ' he repeated.
`And what would you swear? ' asked Frodo.
`To be very very good,' said Gollum. Then crawling to Frodo's feet he grovelled before him, whispering hoarsely: a shudder ran over him, as if the words shook his very bones with fear. 'Sméagol will swear never, never, to let Him have it. Never! Sméagol will save it. But he must swear on the Precious.'
'No! not on it,' said Frodo, looking down at him with stern pity. 'All you wish is to see it and touch it, if you can, though you know it would drive you mad. Not on it. Swear by it, if you will. For you know where it is. Yes, you know, Sméagol. It is before you.'
For a moment it appeared to Sam that his master had grown and Gollum had shrunk: a tall stern shadow, a mighty lord who hid his brightness in grey cloud, and at his feet a little whining dog. Yet the two were in some way akin and not alien: they could reach one another's minds. Gollum raised himself and began pawing at Frodo, fawning at his knees.
'Down! down! ' said Frodo. `Now speak your promise!'
`We promises, yes I promise!' said Gollum. 'I will serve the master of the Precious. Good master, good Sméagol, gollum, gollum!' Suddenly he began to weep and bite at his ankle again.
But then it's foreshadowed directly when they're at the black gate:
But I warn you, Sméagol, you are in danger.'
'Yes, yes, master! ' said Gollum. 'Dreadful danger! Sméagol's bones shake to think of it. but he doesn't run away. He must help nice master.'
'I did not mean the danger that we all share,' said Frodo. 'I mean a danger to yourself alone. You swore a promise by what you call the Precious. Remember that! It will hold you to it; but it will seek a way to twist it to your own undoing. Already you are being twisted. You revealed yourself to me just now, foolishly. Give it back to Sméagol you said. Do not say that again! Do not let that thought grow in you! You will never get it back. But the desire of it may betray you to a bitter end. You will never get it back. In the last need, Sméagol, I should put on the Precious; and the Precious mastered you long ago. If I, wearing it, were to command you, you would obey, even if it were to leap from a precipice or to cast yourself into the fire. And such would be my command. So have a care, Sméagol!'
Sam looked at his master with approval, but also with surprise: there was a look in his face and a tone in his voice that he had not known before.
There's this passage right outside Mt. Doom:
With a violent heave Sam rose up. At once he drew his sword; but he could do nothing. Gollum and Frodo were locked together. Gollum was tearing at his master, trying to get at the chain and the Ring. This was probably the only thing that could have roused the dying embers of Frodo’s heart and will: an attack, an attempt to wrest his treasure from him by force. He fought back with a sudden fury that amazed Sam, and Gollum also. Even so things might have gone far otherwise, if Gollum himself had remained unchanged; but whatever dreadful paths, lonely and hungry and waterless, he had trodden, driven by a devouring desire and a terrible fear, they had left grievous marks on him. He was a lean, starved, haggard thing, all bones and tight-drawn sallow skin. A wild light flamed in his eyes, but his malice was no longer matched by his old griping strength. Frodo flung him off and rose up quivering.
‘Down, down!’ he gasped, clutching his hand to his breast, so that beneath the cover of his leather shirt he clasped the Ring. ‘Down you creeping thing, and out of my path! Your time is at an end. You cannot betray me or slay me now.’
Then suddenly, as before under the eaves of the Emyn Muil, Sam saw these two rivals with other vision. A crouching shape, scarcely more than the shadow of a living thing, a creature now wholly ruined and defeated, yet filled with a hideous lust and rage; and before it stood stern, untouchable now by pity, a figure robed in white, but at its breast it held a wheel of fire. Out of the fire there spoke a commanding voice.
‘Begone, and trouble me no more! If you touch me ever again, you shall be cast yourself into the Fire of Doom.’