However the Silent Watchers, while extraordinarily sensitive to psychic impressions, are in practice prone to giving out false positives. This is such a common problem that lower priority Silent Watcher alerts are routinely ignored despite strict instructions to the contrary. The Silent Watchers are also not good at determining intruder type and exact location, especially outside of close range. The tales of armed patrols being sent to detain ordinary unaligned squirrels and swarms of butterflies are as unending as they are detrimental to the discipline.

We can quite sensibly discuss that Aragorn might well be wieighing up the best plan to get into Mordor as he distractedly drifts down the Anduin and thinks he might have to lead Frodo there.
But (as folks have already said or implied) while it is fun to speculate, there's little chance of working out what he was thinking; let alone figuring out whether it might have worked.

We don'' have to work out under what circumstances Aragorn may attempt the Leap of Beren, and what dice roll is required for success. Or how much damage he sustains if he can't grab something ...load-beren at the top.
Nor whether he falls for an offer of "There's Whiskey in the Jar" offer from those guard orcs, until he gives them an account of his mission as "Musha Ring dumb a do dumb a da...".

They say if you work hard you'll get better pay.

We've heard all that before.

Clean up your buttons and polish your boots,

Scrub out the barrack room floor.

There's many a rookie has taken it in, hook, line, and sinker an' all.

You'll get no promotion this side of the ocean, so cheer up my lads, bless 'em all.
[but at least]
...Nobody knows what a twirp you have been, so cheer up my lads, bless 'em all.

Now Orcs have passed south through Nargil pass in the Southland beyond Harnen.

The forces of Sauron have crossed the Nargul ? Pass and raised the men of Harad and of ? Umbor.

It was a key episode when Southrons and their oliphaunts were marching north to the Morannon but were waylaid by Faramir's men just as F&S were in the vicinity. It wouldn't make sense that they'd skip a more handy southern pass that was a shortcut. I'm sure an argument could be made for it, but still seems flaky in my mind, so better left forgotten.

I personally have long wondered if Sauron communicated with Rhun and Harad by sending messengers into eastern Mordor were there were no mountains, then they could go north or south and not be witnessed by Gondor (unless by palantir).

Anyway, thanks for sharing that with us. Because on its own, it does make sense (in early drafts) that Sauron would have a more direct route to Harad. We can see Tolkien's part-Vulcan mind working logically as he crafted his stories.

Realistically, were there many practical options for Aragorn to lead Frodo and Sam into Mordor? I can only think of a handful:

1. The Black Gate. Too risky; it would have to rely on disguise and deception.This would almost certainly fail.
2. Minas Morgal. Same as above.
3. The pass of Cirith Ungol. Between the Phial of Galadriel and Aragorn's fighting prowness, this would be dangerous but doable.
4. Circumvent either the Ash Mountains or the Mountains of Shadow and enter Mordor from the East. This would take too long, would require extra supplies, and would pose too much risk of discovery.
5. Enter through some other secret or little-known pass that might be unguarded or at least poorly guarded. This might be feasible if such a pass existed. However, we have no solid evidence that this is the case.
6. Enlist the Great Eagles to fly to Mount Doom. There's a good chance that the Eagles would refuse. Aragorn would probably be unaware yet that the Ringwraiths were using winged mounts. Nonetheless, Eagles could be spotted from the ground, triggering an alert. Also, there is the possibility that the Ring could corrupt even one of the great raptors, esp. as Mount Doom drew near.

Have I overlooked anything?

...after the British army song that Tolkien is bound to have known, (entitled Bless 'em all: in the 'radio edit' at least...)

‘What shall we do with the Ring...
'That is the purpose for which you are called hither. Called, I say, though I have not called you to me, strangers from distant lands. You have come here and here met, in this very nick of time, by chance as it may seem. Yet it is not so. Believe rather that it is so ordered that we, who sit here, and none others, must now find counsel for the peril of the world.

Yes, sooner or later - later if he is strong or well-meaning to begin with, but neither strength nor good purpose will last - sooner or later the Dark Power will devour him.

(my italics)

'Yet the way of the Ring to my heart is by pity, pity for weakness and the desire of strength to do good.'
--Gandalf to Frodo

'You’d stop them digging up the Gaffer and turning him adrift. You’d make some folk pay for their dirty work.’
‘I would,’ she said. ‘That is how it would begin. But it would not stop with that, alas!
--Sam and Galadriel

Already the Ring tempted him, gnawing at his will and reason. Wild fantasies arose in his mind; and he saw Samwise the Strong, Hero of the Age, striding with a flaming sword across the darkened land, and armies flocking to his call as he marched to the overthrow of Barad-dûr. And then all the clouds rolled away, and the white sun shone, and at his command the vale of Gorgoroth became a garden of flowers and trees and brought forth fruit. He had only to put on the Ring and claim it for his own, and all this could be.
--Sam in Mordor

...and he caught Deagol by the throat and strangled him, because the gold looked so bright and beautiful. Then he put the ring on his finger.

Boromir got up and walked about impatiently. 'So you go on,' he cried. 'Gandalf, Elrond–all these folk have taught you to say so. For themselves they may be right. These elves and half-elves and wizards, they would come to grief perhaps. Yet often I doubt if they are wise and not merely timid. But each to his own kind. True-hearted Men, they will not be corrupted. We of Minas Tirith have been staunch through long years of trial. We do not desire the power of wizard-lords, only strength to defend ourselves, strength in a just cause. And behold! in our need chance brings to light the Ring of Power. It is a gift, I say; a gift to the foes of Mordor. It is mad not to use it, to use the power of the Enemy against him. The fearless, the ruthless, these alone will achieve victory. What could not a warrior do in this hour, a great leader? What could not Aragorn do? Or if he refuses, why not Boromir? The Ring would give me power of Command. How I would drive the hosts of Mordor, and all men would flock to my banner!'

Boromir strode up and down, speaking ever more loudly. Almost he seemed to have forgotten Frodo, while his talk dwelt on walls and weapons, and the mustering of men; and he drew plans for great alliances and glorious victories to be; and he cast down Mordor, and became himself a mighty king, benevolent and wise.