"Gandalf, instead of walking the ring into Mount Doom, why not ask those giant eagles Uncle Bilbo told me about and fly there?"
The wizard thought it over, and decided it did sound like an idea with a higher chance for success. Plans changed.
Events proceeded, with one crucial difference. After Elrond's they headed into the high mountain passes, seeking the Eagles. They did not venture inside to Moria, instead Gandalf called upon his old friends and they flew to another war counsel in the high aeries.
At first, the Eagle refused, for they were near extinction and preferred neutrality. Then Frodo made an impassioned plea, backed by good friend Boromir, who had become determined to fly with the small hobbit for the glory of all mankind.
Finally the younger eagles broke with tradition and volunteered, against the wishes of their Elders. It was a stealth mission. The larger the group of Eagles, the easier it would be for them to be detected. The group lined up like this:
Eagle Leader: Legolas to guide them with his elf eyes
Eagle One: Gandalf to lead with his wisdom.
Eagle Two: Merry and Pippin for scouting ahead
Eagle Three: Boromir and Frodo
Eagle Four: Gimli and Sam
Eagle Five: Aragorn, with his bow in the rear, covering their backs
At first, Sam wanted to be near Frodo, but have a capable fighter guarding the Ring was deemed much more important. Merry and Pippin loaded their bird up with sling stones, until it was bearing the heaviest load of all.
With due haste, the Fellowship departed in the air.
Gandalf was the first to leave, for he determined the greatest threat against this mission was not Sauron, but Saruman, a corrupted Istari capable of farscrying using a palantir, the head of Gandalf's order who had fallen into the clutches of darkness. Promising to rejoin them later, Gandalf the Grey went to meet his fate, not having the power of his White mantle of wisdom. He left when he realized Saruman had detected the expedition, after the battle of Giant Dragonflies, which the Eagles endured with no causalities and high spirits.
On the eagle leader, Legolas became the director of the expedition. Without much trouble, they reached the skies above Mordor, but the entire country was encircled by jagged mountains and orc spotting stations. Unnatural, deathly winds protected the skies, another barrier against entry. Navigating a narrow gap between two peaks, the Fellowship engaged a cousin of Shelob, who had made a web across the entire sky passage. Becoming entangled in the web, the Eagle bearing Gimli and Sam defeated the spider, but could fly no more. The dwarf volunteered to cut free his partner, and Sam transferred over to Frodo's bird, despite Boromir's grumbles.
His spider-guard did it's job, and Sauron became aware of their presence. His omniscient eye viewed all of his lands from above, so the flyers were obvious. Only a ground trek would be beneath his notice. Aragon, along with Merry and Pippin stayed behind to buy them time against the wave of Nazghuls. Nearing Mount Doom, Legolas engaged the last Nazghul Sauron held in reserve, and the orcs firing Wargs on their catapults proved ineffective. The birds cawed in derisive laughter as the wolves splattered the landscape.
Then the most valiant Eagle carrying the ringbearer proved it's worth beyond measure as it outflew Sauron's dragon, in a dazzling feat of maneuverability. The great lizard impaled itself upon a jutting mountain outcropping. Sam was sick over the side.
Nearing the volcanic maw, Boromir chose this moment to make his move for the Ring. In a fierce struggle, he cut Frodo's necklace after undoing the other precautions, but Sam, dependable Sam, cut the man's leather harness grips, and Boromir fell screaming of man's glory.
The Ring was free, and it could sense it's true master's closeness. It slipped from the hands of both hobbits, fell out of the leather cord, only to be caught in the Eagle's beak. It lodged in the throat of the flying juggernaut, attempt to suffocate and bind the remnants of the Fellowship. The great bird swallowed it, lest it fall into the hands of the enemy.
And so the ring began influencing the Eagle. Frodo and Sam realized what was happening, and sent their ride into a death dive atop mount doom, straight at the bubbling lava. They were crying as they stabbed the faithful bird with daggers.
Sauron was aware of everything, his Nazghuls victorious, and himself having an ample ten minutes to move. He was waiting atop Mount Doom. He didn't even need magic eye lasers, or soul-polluting storm winds, though his lore was capable of both.
He called for his Ring. It ripped itself out the bird's stomach, shedding the blood and bits of intestine in mid air, as the remnants of the Fellowship crashed into lava lake inside Amon Amarth.
The one Ring settled comfortably on the hand of its true master, falling elegantly from the sky.
And ever-after Sauron ruled Middle-Earth with an iron, Ringed fist.