I get a fair amount of that kind of work too, on bass. Mostly jazz, where the repertoire of "standards" is finite. I also go to fiddle jams, where the fiddlers themselves often have no idea what the harmony should be, or how to express that information.
Of course a trick that a layperson might not notice, is that the notes are nowhere close to random.
But I love the challenge of that kind of work if it's with good players.
I guess all that memorization is like the conditioning and training that an athlete might do to prepare for an event, and then at the event you're mostly responding conditions.
And it went OK! In addition to the mental model that you describe, I've also learned that most tunes are more forgiving of changes than one might guess by all of the chord symbols notated so precisely.
I've revived my fake books for another use: To practice treble clef sight reading, which I neglected when I was younger. Also, I think learning melodies helps a lot in terms of mentally organizing and navigating the standards.
There are players who are a lot better than me, and are still attached to the books.