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These are good questions.
As an example of something that didn't seem 'beyond' LW, Rand's Razor seems like a useful habit for dispensing with perverse concepts like grue and bleen, but Follow the Improbability feels like the better version of it. Like, how is 'necessity' measured?
Ayn Rand wrote a ton of material on concept-formation: some of it is in ITOE, and some of it is scattered amongst essays on other topics. For example, her essay "The Art of Smearing" opens by examining the use of the flawed concept "extremism" by certain political groups to attack their opponents, and then opens out into a discussion of the formation of "anti-concepts" in general, and their effects on cognition. She has several essays of a similar nature.
The downside of such an approach is that there isn't one unified resource you can point people to that explains Objectivist epistemology in detail.
Objectivist epistemology is hard to summarize -- it includes some useful cognitive heuristics (like "Rand's razor" and the idea of checking for "package-deal" concepts or other invalid concepts), but the whole package includes a lot more than those heuristics. It's also integrated down to philosophical fundamentals -- including, most notably, an attempt at carving a third position to the Platonism vs. nominalism debate over universals in traditional philosophy. However, that is quite hard to summarize in a comment. The best resources I can point to are either ITOE (which is admittedly dated), or Harry Binswanger's book How We Know.
But just for the purposes of illustration, the Objectivist answer to the grue/bleen issue would be that blue and green are the more basic concepts because they are directly derived from perceptual experience. (Following Aristotle, Objectivism holds that perception is the ultimate base of all knowledge.) The idea that "a green object may turn blue for some unknown reason at some future date" is an arbitrary claim with no evidential basis. If a given green object did change colour, one should determine the cause of the colour change prior to defining a new concept to categorize the object under. (And, realistically, given present scientific knowledge, there isn't much reason to believe that any given object will begin changing colour for no known reason.)
Likewise, the Objectivist answer to the blegg/rube issue (https://www.lesswrong.com/posts/4FcxgdvdQP45D6Skg/disguised-queries) would be that there is too much overlap between the two concepts (as presented), and that therefore the two concepts are not valid. This is not to say that there is no distinction between the objects, but, absent any knowledge of why certain properties tend to appear together, the individual objects being categorized would be better described as simply "palladium-containing, blue, egg-shaped object" or whatever.
One does not form concepts simply by clustering together objects with similar properties, but also by identifying causal connections between the properties. In the case of bleggs and rubes, if one could show that the fact an object contained palladium tended to cause it to be blue and egg-shaped, then you would have a basis for forming an objective concept of "blegg".
Compare with examples in biology, where there is no confusion over whether, say, a duck-billed platypus is a bird or a mammal.
The platypus shares similar properties with other mammals because of a similar underlying cause (it has similar DNA, due to shared ancestry) but has some differences with other mammals, because it is further away on the biological "family tree" -- but its most recent common ancestor with the other mammals is far more recent than with the birds or reptiles, so it should objectively be categorized as a mammal. On the other hand, Objectivism also agrees with LW in holding that there is no answer to the question of whether a certain object is really a blegg, or whether a certain animal is really a mammal. All concepts are simply human-created categorization schemes, evaluated by the extent to which they track genuine distinctions in reality (a genuine distinction, such as that between mammals and birds, usually being supported by the identification of an underlying cause that gives rise to the distinction, such as differences in DNA).
As you can see, this is only scratching the surface of a very complex topic, so I'll leave the above as simply an indication of the Objectivist approach. Otherwise, yes, you are correct that there's a decent amount of material in the modern-day "rationality corpus" that isn't integrated into Objectivism.
(Edit: I just read the linked SSC article that discusses Aristotelian epistemology. His description doesn't really apply to Objectivism, which says that knowledge is reached via induction (from observations), not deduction -- though many Objectivists, like Scott's campus Objectivist friends, unknowingly practice the wrong methodology (e.g., misuse of logic and overuse of deductive reasoning). Likewise, though Objectivism holds that (contextual) certainty is possible, it also makes clear that claims can also be classed as "possible" or "probable", with probability increasing as evidence is accumulated. Finally, because knowledge is integrated, if one of your beliefs is proved wrong, one should seek out other related beliefs that may now be disproved.)
It would be interesting to work on an integration of Objectivism with more modern approaches, though I personally have other projects to work on which are more of a priority for me personally. However, I've pondered the idea of setting up an online community that would be a kind of gathering place for such work.
As for the other comment's question on practical uses of Objectivist epistemology, off the top of my head I can think of: The Logical Leap by David Harriman (an attempt at solving the problem of induction), the startup Mystery Science (elementary science education based on an Objectivist approach), Jean Moroney's website/consultancy Thinking Directions (similar type of material to CFAR) and Boom Supersonic by Blake Scholl (supersonic jet startup, Blake said he developed the original idea by applying some of Jean Moroney's thinking techniques).
Hi - this was a very interesting post to read. I'm an Objectivist and former LW-lurker and rationalist-adjacent, so it's interesting to see how Atlas Shrugged reads to someone from the LW-sphere who is sympathetic to some of the core ideas, but not all of them.
My background (for the curious): I binge-read the sequences a few years ago, along with many other writers in the rationalist diaspora (along with other contrarian thinkers, such as Nassim Taleb, David Chapman, and so on), but was eventually sold on Objectivism after reading Ayn Rand's book on epistemology (linked below).
At one point I wanted to work on a comparison or integration of LW-style ideas with Objectivism. I think that project would be too big, but there's almost certainly much untapped value available to anyone who wants to investigate the connections between the two epistemic communities. For now, I'll just link to some of the central writings by Ayn Rand and other Objectivists, allowing people to form their own judgements and giving curious minds a few "rabbit holes" to explore.
Basically -- the element of Objectivist philosophy that is by far and away the most useful is the epistemology. The material on politics, though important, can be something of a distraction, as Objectivists are just as prone to being mind-killed as others, and the usual focus on politics whenever Ayn Rand is discussed usually creates lots of drama and distracts from her more fundamental philosophical ideas.
Objectivist epistemology is basically a modified version of Aristotelian philosophy, one that doesn't rely on any kind of quasi-Platonist metaphysics. In simpler terms: it holds that concepts are cognitive tools for grasping reality successfully, and that discovering truth is essentially a process of observing reality, forming valid concepts and then integrating one's concepts correctly. Grasping the epistemology is really the basis for understanding the rest of Objectivism, and will help you understand on a deeper level the philosophical issues mentioned in your post.
Anyway, my recommended reading list:
Fiction
Aside from Atlas Shrugged and the Fountainhead, Ayn Rand also wrote a novella called Anthem, a dystopian sci-fi text in the vein of 1984 and Brave New World. It's available online and a quick read:
https://www.gutenberg.org/files/1250/1250-h/1250-h.htm
She also wrote a semi-biographical novel, We: the Living, but I haven't read it and can't vouch for the quality.
Non-Fiction
The vast majority of Ayn Rand's non-fiction writing is in the form of essays. Most of these have been published in various essay collections, but not all of the essays in these collections relate directly to her core ideas. Below are some of her core philosophical essays:
Core essays
The Objectivist Ethics (meta-ethics) https://courses.aynrand.org/works/the-objectivist-ethics/
What is Capitalism? (politics/economics) https://courses.aynrand.org/works/what-is-capitalism/
Philosophy: Who Needs It (general philosophy) http://fare.tunes.org/liberty/library/pwni.html
Who is the Final Authority in Ethics? (explains the concept of "objectivity") https://courses.aynrand.org/works/who-is-the-final-authority-in-ethics/
Non-fiction books
If you want a more comprehensive understanding of Objectivism, a good "mid-level" introduction is the essay collection "Philosophy: Who Needs It".
The best advanced introduction is the book "Introduction to Objectivist Epistemology", which (unsurprisingly) discusses the fundamentals of epistemology. Chapter 1 is available here: https://courses.aynrand.org/works/cognition-and-measurement/
Book here: https://www.amazon.com/Introduction-Objectivist-Epistemology-Expanded-Second/dp/0452010306
Then there's "Objectivism: the Philosophy of Ayn Rand", which is the book that explains all the branches of the philosophy in detail.
All of these are available on Amazon.
Other resources
The Ayn Rand Lexicon has an index of core concepts: http://aynrandlexicon.com/book/conceptual.html
The Objective Standard has a good "layman's introduction", along with a bunch of other good articles: https://theobjectivestandard.com/what-is-objectivism/
Books by other writers
There's been a bunch of books written by other writers that build on Ayn Rand's ideas. I'll just list some key ones (all available on Amazon).
Viable Values by Tara Smith: more academic survey of Objectivist meta-ethics
How We Know by Harry Binswanger: more comprehensive book on epistemology
Ominous Parallels and The DIM Hypothesis by Leonard Peikoff: philosophical analyses of cultural change
The Logical Leap by David Harriman: theory of induction based on proper concept-formation
Some more technical writings on philosophy are available here (including Greg Salmieri's attempt to integrate Objectivism with more traditional Aristotelian philosophy): https://aynrandsociety.org/books/
And I think that covers all the bases. Oh, one final one: Robert Transinski's book on Atlas Shrugged has some unique perspectives on the book, so should be relevant to OP: https://www.amazon.com/dp/B07YCY22W8/
By the way, I'm a big fan of the Lesswrong model -- there are a bunch of Objectivist online groups and forums, but nothing of stellar quality, and I find the Lesswrong platform and community tends to encourage good epistemic norms. If anyone's interested in some kind of cultural cross-pollination between the two groups, let me know, because I think it would have a lot of value.