it would clear in seconds with a/c - that's one of it's key functions
the reason it works as the a/c makes the evaporator cold, so any moisture in the air condenses on it so that the air coming off it is very dry.
the downside is, that the moisture stays on the evaporator after the a/c is switched off, so it gets blown up onto the screen and mists it up again. it's a viscious circle.
if you can, dry the evaporator sometime by running the fan at full speed, with the heater on full blast pointing at the floor vents and in recirculation mode with the windows open.