Ahem ... OK, I've come up with some new stair designs that won't bite. Now I need to know if they don't bite.
Insight #1 was realizing that stairs are a lot more useful if they have a label showing what off-map area they lead to. In that case whether they lead up or down will be self-evident.
Insight #2 was that old-school 1e DMG style stairs are not ambiguous when they disappear into black map rock. So a way to show their third dimension when they're in the middle of a floor would use a black outline, thicker at the "disappearing" point off-map.
As for the spirals, the most useful thing about them, I realized, was the "landing" showing where you could get on the stair from the floor being mapped. So I cut a pie wedge out of the traditional icon ...
The one on top spirals up and down, while the lower left one leads up and the lower right one leads down. The arrow always points gravity-ward, a convention from my slope arrows.