I would propose funny solution to change the room where 312hz will fall into one of the standing wave frequency. Then if you combine properly where to place fan and where to place your sit, you can achieve effect of cancelling at this frequency/position (and amplifying in other positions)
Since a room has reflections and diffraction of the sound waves, the 312hz they're trying to dampen w/ ANC will be at different phases at different parts of the room. It's also not a point source.