I just solved this issue! The problem is not that the screen is "somehow" rendering the proximity sensor useless, the problem is that, if you look closely enough, you will see that the transparent holes on the screen that the proximity sensor use are not "centered" in the socket. Therefore, the proximity sensor is not working.
With a sharp point, remove the holes (not all the way to the edge of the socket) and paint with a black permanent marker. The proximity sensor works again!
Surely, this relates to poor manufacturing!