I have a cheap dash cam, about £15 a year or two ago. It works remarkably well apart from the time and date changing in an odd way.
However there's always a shadowy image of the vent grille below, reflected by the windscreen.
I think a polarising filter would fix this, it certainly works for my eyes with polarising sunglasses. Problem is getting something to fit nicely.
But what about some anti-reflective film on the windscreen in front of the camera? Would that work?