Another Dice Tower Split Staircase

When I initially began printing Lau85's "Another dice tower", I encountered difficulties with the spiral staircase portion of the model.

I was opposed to using so much filament on support, and the design of the staircase indicated that so long as I had really good bed adhesion, that it should print successfully without supports. I decided to add a 10mm brim when I sliced the part, and it appeared to do really well as it printed, until... at just above the 80% mark, the model was knocked by the print nozzle and partially separated from the brim, allowing the mostly printed staircase to topple over.

Thinking that the problem was merely a fluke, I reprinted the staircase and had the same result. I then expanded the brim from 10mm to 30mm and enabled Z-hop. The staircase then printed and completed successfully.

I gave the first dice tower I made to a neighbor and printed it again for myself. The same model, using the same gcode files I'd sliced for the first print failed agai