Push up to enter the background of the scene for ascending/descending stairs, move forward just enough that your character switches into the "stepping" animation on the first step, then push down to move back to the foreground. The character is now incapable of climbing stairs until you fast travel or leave the area.

I can do this 100% of the time in the living quarters, but it doesn't seem to work in other areas. I think this is because the bounding box for the foreground/background transition doesn't cover the edge of the steps in other areas. I hit this bug twice in my playthrough so far so I tried to reproduce it. lol