What is needed is that a flow of outside clean air (pressurized and warmed) that flushes from the cockpit to the rest of the plane.
That is already done on the B744. The flow of air into the flight deck is higher than the rest of the aircraft and so air vents from the flight deck to the cabin. This does not cause an overpressure but does cause a positive airflow from the flight deck.
Opening the smoke evacuation port is only useful if the smoke is generated on the flight deck. Otherwise opening this port will reverse the positive flow, and draw air in from the cabin.
Dave