... Which is of course nonsense.
Of course. Because it is nonsense to talk about something that we cannot measure. But then, you proposed a way of determining the path of the electrons.
If we can make the first screen movable, so that it's knocked out of position whenever an electron goes through it, we could determine in which direction the electron was going. If the screen moves downward, the electron is going through the top slit.
If the screen moves upward, the electron is going through the lower slit.
Thus we could satisfactorily determine both the position and the velocity of the electron. Now we would know more about the path of the electron than the Uncertainty Principle allows. Quantum mechanics is incomplete. Which was to be demonstrated.