[Otto]

This seems akin to buffeting on a faired motorcycle, where von Karmann vortices form and collapse behind the screen, dope-slapping the rider in the face. Just like on my BMW R1100RSL. Key to fixing this is either a hugely larger screen such that the vortices collapse well behind the rider's head, or channel air up the backside of the screen to relieve the low pressure bubble and then flow up and off the leeward side of the upper screen edge, such that it meets the flow coming up and over the front side at nearer the same direction and velocity, reducing wind shear for less dope-slapping in the face.

So, I'd say that the red flap in Big Time's car might work. Or add a pop-up castellated deflector like on the leading edge of BMW sunroofs, or similar.