I ran into this same issue, and honestly thought, due to how close, yet so far, and obvious the solution was, that I'd triggered an Anti-piracy check, that gave a false positive, to the point I was going to remove and re-buy it.

Thankfully, looking at it today, I had a very large "AHA!" moment that quickly followed into a "My gods I'm an idiot..." sentiment, after I realised how shortsighted I was in trying to solve it.

Which is to say that the stage is completely doable, and that I not only have the solution, but recorded it, so that you, and anyone else that may get stuck can see what to do: https://youtu.be/AxeGQK2V_yU