An idea I had was that if the "gallery" and the "alcove" were both laid out on hexagons of the same size, it makes things pack better -- or at least makes the voids between galleries always be hexagonal, instead of other weird shapes, and that pleases me.
Here are two contradictory phrases that occur in the text "narrow corridor" and "spiral staircase". Spiral staircases are huge. They have to be. That's kind of their thing. So I tried to pack things down by putting the staircase off-center, walled off, and that works out ok, except it adds packing constraints: the stairway no longer lines up if the alcoves above or below this one has been rotated. So that severely limits the variety of layouts available.
And here are a bunch of them, all aimed in the same direction, because the two doors on each gallery are opposite each other:
So maybe that wasn't such a good idea. So I went back to a central, symmetrical spiral staircase. Here's what that looks like, with every room having a 101110 layout, creating six-gallery loops:
And here are three floors of it: to make this connect, each spiral staircase would span two floors:
If you want to play around with other layouts, here's my Sketchup file: babel.skp.
Update: Now with smaller and more treacherous stairs, narrower hallways, and hallways that turn!