That post was getting long... and I did not even comment upon the theology of Sauron's strategy.
Sauron was a fallen angel. As a Maia, created by Eru, Sauron was there for Melkor's first and second songs. He was sent to Arda with the Valar. But at some point he joined Melkor against the Valar. He escaped destruction and judgement in Melkor's defeat in the unnumbered years and in Melkor's defeat in the First Age. He achieved the destruction of Numenor, the defeat of Ar-Pharazon, the subversion of the Noldorin revival in Eregion, the death of Celebrimbor, the death of Gil-galad, and the deaths of Elendil and Anarion all in the Second Age.
The Rohirrim, the Hobbits, the Dwarves and most others (notably Boromir and Denethor, and probably Saruman and Radagast as well) viewed the clash with Sauron as geo-political. Only a few, like Elrond, Galadriel, Cirdan, and Gandalf attempted to keep a holistic view of things.
Why would a fallen angel who used to live in the very presence of his creator attempt to hold temporal power? He watched his old master, the mightiest angel ever, attempt the same thing and fail, defeated by the angels of the creator. How could he think he could do better? What is his end game? What does he get out of it? To rule as a mortal king... that's stupid because he's an immortal super powerful being. Wealth? No. Women? No. Worship? Not exactly.
The men of the White Mountains swore allegiance to Isildur in the Second Age. When he called them to uphold their pledge and join the Last Alliance, they reneged. The Return says something like... "...they worshiped Sauron in the dark years..."
I think in The Akallabeth it says something about Sauron being both god and king to the men of Middle-earth.
I think he partly reveled in watching people abase themselves before him and fooling himself that he was the greatest, but I think secretly he enjoyed knowing that he was continuing to corrupt Eru's plans and thwart the efforts of the Valar. Sauron had become thouroughly evil. Misery loves company.
If Sauron could achieve a total victory over the Eldar, the Dunedain, and the Khazad, then maybe he thought he'd be left alone by the Valar.
But even with Melkor's victories over the Noldor, and the destruction of Doriath, Hithlum, Nargothrond, Gondolin, and the havens, and the deaths of Finwe, Feanor, the sons of Feanor, Fingolfin, Fingon, Turgon, Finrod, Luthien, Beren, and all the heroes of the Edain, and the departure of Melian... the Valar did not leave him alone. Earendil and Elwing (their ancestors combined all the royalty of the Noldor, the Teleri, and the Edain) escaped and pled their case before Manwe.
All of Sauron's victories still could not quench the line of Elros. Elendil survived the foundering of Numenor. Valandil was not present at the Gladden Fields. Aranarth did not flee to Forochel with Arvedui, Last King. (When Ondoher of Gondor and his sons were slain by Easterlings, his third cousin thrice removed, (I don't really know if that's the correct degree) Earnil assumed the throne, but his son Earnur was lured into a trap by the Witch-king and was never seen again.) Arathorn II impregnated his wife, Gilraen, a month or so before he was killed by orcs.
How do the descendants of the kings of the Noldor, the Teleri, the chiefs of the Edain, and the kings of the Dunedan continue to survive in the face of direct targeting by Morgoth, Draugluin, Glaurung, Sauron, and the Witch-king? It's supernatural. Call it the will of Eru. Call it the blessings of the Valar. Call if Providence. I see it as evidence of the continued subtle involvement of the Valar.
The Valar sent the Istari (Saruman, Gandalf, Radagast, and two unnamed others) to help rally the Free Peoples and stir hope and courage in their spirits. It was this supernatural battle that Sauron could never win. Even though Sauron's assaults failed, he could recruit faster than his enemies and do it again... and again... and again until he won. Like Grant versus Lee and the Soviets versus the Nazis, Sauron's enemies could not endure their pyrrhic victories for long.
Sure, the Valar could always come over and defeat the evil overlord du jour, but what about the next one? I think they found it better to encourage the people of Middle-earth to stand up for themselves. "Just fight the good fight... while we sneak the Ring right past Sauron's wandering eye."
Sauron understood might. That's why his armies are like sledgehammers. He understood the danger that mighty Numenorean could pose.
Who among the mighty of the Third Age was born to the ruling family of the strongest opponent to Sauron? Boromir.
Who was educated to command on the battlefield? Boromir.
Who was educated to lead a nation in it's continuing age long struggle? Boromir.
Who was leading men in battle at a young age? Boromir.
Who was commander in chief of his nation at a young age? Boromir.
Who held the symbolic horn of the heir of the rulers of Gondor? Boromir.
Who held the bridge at Osgiliath from Mordor's assault? Boromir.
Who undertook the quest to save Gondor? Boromir.
Who was the most qualified person to oppose Sauron by bringing Frodo and the Ring to Mount Doom?
Sauron certainly thought the answer to the last question was Boromir. Once Boromir fell, his minions targeted Faramir. When Aragorn showed himself to Sauron in the palantir, Sauron suddenly changed the answer to all of these questions to Aragorn, Isildur's Heir. Fearing Aragorn (maybe with Arwen at his side) might sneak up on him like Beren did to Morgoth or challenge him directly like Feanor or Fingolfin or bring about his demise by some errand to the Valar like Earendil or set himself up as King of Arda as Ar-Pharazon. Saruron confounded by the revelation of Strider as Aragorn Telcontar, Elessar the Renewer, the Elfstone orders his assaults before he's fully prepared.
So who was the most qualified person to oppose Sauron? Samwise Gamgee.
The wise could not have forseen it...
Yes, Sam embodies British common sense. But he's also the chosen champion of Varda Elentari, Queen of the Valar, Queen of the Stars, Elbereth, Gilthoniel, Fanuilos... her gifts are light and grace. Just like Athena, Ares, and Apollo endowed their Greek and Trojan champions with courage and strength, Varda does this for Sam... and Sauron never saw it coming.
I think Sauron was so caught up in focusing on the descendants of his enemies and the ways that the Valar might use them, that he forgot that they could use anyone. And this is why I don't think Tolkien is a pantser... I don't see it as deus ex machina at all. I see the continual success of Frodo and Sam against insurmountable odds as the blessings of the Valar, the will of Eru, or Providence.