The windscreen is an air dam. Too flat and vertical so air swirls over it and into the cockpit. Like the rear of a van/hatchback. Improved airflow over the windscreen would help but not cure the forward flow on passengets heads. More rake to windscreen? Higher?some way of catching and diverting the air as it passes over? Not easy without altering the car's profile/ styling. I have a windbreak for behind my head but had to remove it for a rollbar. I may alter it to try it again, but didn't find it hugely successful when it fitted. So...it's hat/scarf/wipe any dirt for now.
