Idioms – Meaning of ‘Keep Something In The Know’

Your first instinct is correct; this is a noun adjective construction. It does indeed look like the keep something in some condition construction, but that doesn't make sense semantically. It's keep in the sense of retain possession, which is often used to indicate that something else is more desirable or better, as is the case here. The Hogwarts Sorting Hat is the best hat there is, so "you" can keep all the other hats, as they are unnecessary.

Why is the usual word order reversed? Because this is a poem and the author wants to maintain a meter. Black bowlers would make two stressed syllables sequentially spoken, and break the rhythm.

How much water a boat draws is a measure of the depth of water required to float it: a rowboat ‘draws’ only a few inches, a fully loaded flat-bottomed barge may ‘draw’ eight or ten feet, an ocean-going vessel with a very deep keel may ‘draw’fifty feet.

Figuratively speaking, how much ‘water’ a man ‘draws’ is a measure of his presence and influence. Jackie Treehorn is a very important man in his community; Lebowski is a nobody.

• ADDED:
  Galactic Cowboy suggests that the idiom here is one of drawing water from a well or other source, and that in water-poor Southern California a man entitled to "draw a lot of water" is marked as particularly influential. He may well be right: one of the earliest instances I have found of the idiom is from a 1938 crime novel set in LA and written by a former LA policeman in 1938 - about ten years after the California Water Wars. One seamier sidelight of that episode was the profits supposed to have been realized by insiders who bought up land in the San Fernando Valley, knowing that LA would have to annex the district to secure rights to the water. However, I also find the idiom in a report of an air show in the Pacific Northwest in the same year.