Aragorn decides he doesn't want to be king: Tolkien canonically wrote Aragorn walking away from leadership positions (under the king/Steward) in Rohan and Gondor in his earlier days so there's precedent. Renouncing the throne at the end of the trilogy would be a sign of true humility and a lesson in leadership as noble service, and Aragorn would get over it as soon as everyone convinced him he was noble enough to be a good'un. Maybe Tolkien would throw (another) sword at him as he passed by a lake, idk, but this would be yet another sign of how sparklingly Da Best Aragorn is.
Frodo casually throwing the ring into the fire: A triumph of the eternal fortitude of the English country squire's soul. The ending Tolkien probably wanted for Frodo in his heart, even though he knew he had to stay true to his own wisdom and perspective on Frodo's suffering. Also, Tolkien is a professor at a top-flight elite school so he'd appreciate the reference.
Gandalf reunites with the Balrog: Look Gandalf has a lot of fire-coding in the books, the Balrog is also very fire-coded, and it'd all be very symbolic for Catholic repression and taste for the forbidden. Expect a leather jacket (or pants) and whips or possibly arrows tastefully penetrating torsos to also make their appearances.
Tom Bombadil and Esperanto: I've no idea Tolkien's thoughts on Esperanto but slamming the story to a halt so the wacky part of his subconscious that wrote Tom could lecture us all on another language is really not out of the question here. This would not stand out from the actual canon in any particular way.
Elvish Divorce Court: Look, the Pope and various other high officials could grant divorces for centuries in Catholicism and usually did for marriages with far lesser degrees of consanguinity then what proliferates through the Silm. If anything, maybe that would've been the lesser sin compared to some of the marriages and relationships Tolkien did write. Also, if he'd known the kind of warfare that daytime court tv would be capable of producing, he'd have probably been delighted at all the new angles of conflict he could work into the Silm.
Tax Policies of Minas Tirith and Orc Rehabilitation: He probably wouldn't have cared about the tax portion of this but the man was distressed by the Always Chaotic Evil races he ended up writing. Orc rehabilitation would likely have been inevitable if he'd been granted another few centuries to keep working.
The Shire industrialization: The only one that comes close to Santa. He did write it, and he probably was furious at the idea. But he also wrote the Hobbits putting things back to rights after the Scouring of the Shire, so he did figure out a resolution to this in the end.
Complex Hobbit Polyamory: Sorry, wasn't that already going on in Bag End by the end of the trilogy? Let alone whatever Merry and Pippin had going on between the two of them, their wives, Faramir, Eomer and Eowyn? Tolkien wouldn't've been distressed by this, the idea is pretty integral to his backstory for how he found The Red Book in the first place!
Eärendil's adventures aboard the Starship Enterprise: An idea so foreign to this master of fantasy that he simply wouldn't've understood it enough to become distressed by it. Eärendil did technically have a star ship, and probably adventures, and Tolkien is left asking politely what else is there to this prompt?
Gimli's Cousins: Jokes on all of us when we finally get around to learning Khuzdul and realizing that half of the Company's names break down like this in The Hobbit.
Boromir Lives: Considering Boromir was one of the original four companions of the Fellowship Boromir arguably lived longer in Tolkien's mind than most of his companions. If Tolkien was confronted with a Boromir Lives AU he'd probably shake his head, but understand the wistful longing one could have for the war dead to be among us again. We're not going to think about that too hard.
The answer here is Santa. It's always Santa and it's always going to be Santa. For the simple reason that incorporating a Santa into the legendarium would require, among other issues, working Jesus into Middle Earth somehow and then also a December, a Christmas, and reindeer. There's simply so much work here to do to lay the ground for even asking what you had to do to get Santa into the story that the man would snap and Gondor would probably end up sinking into the ocean or something. Marking the third time that's happened to either a member of Elrond's family or the entire country his relation was connected to. Genuinely, if you asked Tolkien to consider putting Santa into the trilogy I think we'd get the outlines for a Morgoth Redemption Arc instead. He'd just pull him and Feanor out of the void right in time for tea with Uncle Iroh and avoid the big red-suited sleigh-driving jolly saint in the room entirely.
