I'm having a hard time picturing the seating position required to get the screen to reflect on the windshield
Where is the glare located on the windshield at night?
I've never noticed, so i'm guessing it's not really somewhere you'd really be looking while driving.
Rather than tilting the screen, can you fabricate a little shield/hood for the top of the screen to block the reflection? Something out of thick black construction paper.