The disanalogy you quote might actually be the key insight. What if language operates at two levels, like Kahneman's System 1/2?
Level 1: Nearly autonomic — pattern-matched language that acts directly on the nervous system. Evidence: how insults land before you "process" them, how fluent speakers produce speech faster than conscious deliberation allows, and the entire body of work on hypnotic suggestion, which relies on language bypassing conscious evaluation entirely.
Level 2: The conscious formulation you describe — the translator between perception and meaning.
LLMs might be decent models of Level 1 but have nothing corresponding to Level 2. Fedorenko's "glorified parser" could be the Level 1 system.
> LLMs might be decent models of Level 1
I don't think so. Fast speakers and hyponotized people are still clearly conscious and "at home" inside, vastly more "human" than any LLM. Deliberation and evaluation imply thinking before you speak but do not imply that you can't otherwise think while you speak.