Tolkein would have had to construct yet another conflict of the sort which drives LoTR, and he has a limited pallet to draw from (Sauron is pretty much KIA, so now what, Morgoth himself, that means portraying a final 'Armageddon' essentially). Basically he'd have to one-up LoTR too, or it would simply be an afterthought. He's already explored the theme pretty systematically, so it may be possible to deepen the examination, but it would not be anything like the previous story. For instance he could actually explore Melkor (Morgoth) in more detail. Is he really the abominable monster he's made out to be in Quenta Silmarillion? Is he even ultimately 'evil' or is his purpose simply to help drive the ultimate plan of Illuvatar? He would have to start to engage with these deeper questions about the nature of good and evil. Why does the omnipotent and omniscient Illuvatar have evil in his plans if he is supposed to be good? etc. It sure wouldn't be the same simplistic (though Tolkein certainly isn't simple in many respects) free will vs tyranny sort of stuff that makes LoTR go!
So, frankly, I am of the opinion that ME, as envisaged in LoTR at least in its 3rd Age incarnation, is pretty much a single-use setting. Yes, you can tell small 'fairy tale' type stories, even up to the scale of "fighting mighty dragon Smaug" or something equivalent, but the story of the War of the Ring is pretty unique, it cannot be rehashed within that setting in an effective way. Given that Tolkien already wrote There and Back Again (The Hobbit) as a prior story of that ilk he's got even less space. At best another similar tale has to equal or best Bilbo's tale, which is going to be hard to do. Even if he pulled off such a thing its hard to give it the salience that was retconned into the finding of the Ring and Gollum, etc.
I mean, various RPG authors have produced material/systems for play in 3rd/4th Age ME. In my experience it doesn't come off as an especially great vehicle for that. The authors are stuck trying to provide some adventures that turn out not to change anything (because they don't have the authority or desire to establish divergent canon). Tolkien didn't actually describe ME in much detail either. Yeah, there's a bunch of place names and various things can be inferred or are casually mentioned in passing, but the setting is actually profoundly deficient in everyday 'stuff'. Outside of the Shire we get very little to no examination of everyday life or ordinary people. When you start to inject that stuff it tends to mar the high fantasy feel of the setting. In the end my conclusion was that something like WoG, my own homebrew, etc. end up playing pretty much equally well in practice and I have a lot more freedom in my homebrew to define the major conflicts and the nature and feel of things.
I think trying to rehash or oneup LOTR is the wrong approach.
Tolkiens original idea for the sequel started seeding threads about not just people beginning to treat the past with flippancy (children playing as Orcs, on up to cults to them), but also, at least from my reading, the inevitability that the "Shadow" would always crawl back into the world, even without a Dark Lord to champion it.
I think the main reason this didn't get any momentum going is because it doesn't explore anything new; its just a direct reaction to what occurred during LOTR, and one that merely subverts the triumph it without anything meaty and new enough to justify it.
As such if it were me as a writer, I would concur with Tolkiens idea to focus on Men and how their civilization unfolds, but I would set it specifically amongst the backdrop of the last of the old heroes departing Middle Earth in their various ways, and I think Id incorporate a theme of legacy, and how the old "Stewards" of Middle Earth foster one that'll last...or perhaps not?
I think the principle conflict would actually be who should follow and be followed when the old pass on, and I think in that context, you can justify bringing in those themes about flippancy and the resurgence of the Shadow.
And I think this would work; particularly as it happens to have some happy paralells historically with what happened after (IIRC, might be mixing up my monarchs) Charlemagne died.
I think the challenge of it is still, ultimately, in not undermining the triumph. Despite the coming strife of this story, what the old guard did is still fundamentally important and should underscore the conflict pretty starkly. If it were me, I think I'd try to thread that needle by leaning on another theme of combatting cynicism and contempt; the conflict comes from not regarding the past's triumphs with respect and deference rather than from that triumph being undone.
But that diatribe on my thoughts on a LOTR sequel has to be taken in context with the fact that this is all about how we would do this in a book, not an RPG.
Although, much of the same principles apply as far as laying down the essential hook of an RPG that sought to tackle this question, we'd just have to be far less prescriptive about how the specific themes of the conflict play out.
