>Yudkowski has for more than a decade pursued the possibility of perfect human reasoning
His website is literally called "Less Wrong". It's fundamentally a quest for improvement, not perfection.
>His system of coldly logical reason, it turned out, was by many accounts completely undone by a logical paradox known as Roko’s Basilisk.
Roko's Basilisk is a thought experiment designed to import your "don't negotiate with terrorists" intuitions into a really weird corner of decision theory. It's possibly why prior decision theories held were rejected as flawed, but it's not a current issue with their logic. Roko's Basilisk has, unfortunately, gotten way more coverage and fame than it deserves in terms of actual importance. This is because of the regretful (but understandable) decision to censor discussion of it on Less Wrong, which backfired spectacularly.
>For super-nerd bonus points, it’s also arguably a spin on Godel’s incompleteness theorem, which argues that no purely rational algorithmic system can completely and consistently model reality, or prove its own rationality.
That's not at all what Godel's incompleteness theorem argues. That's much more narrowly about formal logic.