Once the character has reached a Lift level of 10 (or perhaps lower), perhaps the mechanic should be turned on it's head: you now introduce a veil/lift for Earth. It may not be that the character is less insane (they still believe in and have a working knowledge of Cthulean lore), but that they can increasingly re-interact with the world that they were born in. This would have the side-effect that those beings whom the character has been working with "on the other side" are now viewing the character the same way that "normal" people had been viewing the character. i.e. not entirely "sane" in the worldview of the Cthulean beings.
Super interesting idea, thank you! And this seems to align nicely with the vague general feeling I had of a direction where things seemed to want to be going! Though I admit that personally I find it a bit difficult to wrap my head around in this way; but maybe that’s a time when an actual playthrough attempt at all of that could give some more clarity 😅