> Okay...
>
> So I'm in the mastermind's study, having raided all the other floors for stuff. I've looked around and around, gone upstairs to check for changes after twisting and pushing, but can find nothing to give me a hint on how to twist that stupid crown to get results! Am I overlooking a crucial clue, or is this just trial-and-error?
>
> You're Carrying:
>
> Matches
> Hat Pin
> Playing Cards
> Rapier
>
> Wood
> Feather
> Map
> String
>
> Altar Cloth
> Key
> Canteen
> Spittoon
>
>
> -Mandi aka Chaos

There a couple things involved, I think. The desk drawers have to be in the right position (which can be determined by looking around for a significant change when they're correct) and then the stuff with the crown. Without saying the exact moves, I can tell you that solving it is probably a matter of trying the correct 2 or 3 moves in the right sequence. It's possible to solve in a surprisingly small number of moves if you do it right from the start, but for all I know it's also possible to do the *wrong* thing from the start and get into an awkward state that you'd need to undo, first. I don't know the internal workings of the puzzle, myself.

My advice is just to take it like all those other AGL puzzles where you get stuck in a confusing sequence -- just keep fiddling around and trying various combinations, and you'll stumble across it eventually (hopefully within a few minutes).