I wanted to post this in Know Issues but I'm not cool enough.
Know Issue: Revit does not support stairs with self-intersecting sketches. There are few very special cases that happen to work - in general, it will not work for now.
Workaround: As a workaround you can create 2 stairs elements without overlapping to achieve proper 3d representation which I believe you had already discovered.
Officially aknowledged: Autodesk Subscription Support Team
Enhanced work around: Start and stop each stair at the middle of a landing. This way the intersection cleans up perfectly each time. Starting and stopping at the spring point can cause issues. Ditto for the railings.