Lu, the clue in your quote from the FAA is "downdraught" - this is not recirculation but turbulence on the lee side of a mountain feature where the air is going downwards and takes the aircraft with it - standard reaction is to turn away from the obstacle(high ground) and establish a maximum rate climb configuration. Then you wait (and pray)that the severity of the downdraught really does reduce as it nears the ground!
Your rocket science sounds like COANDA effect which the NOTAR aircraft use to exploit pressure differentials on opposite sides of the tail boom to produce anti-torque thrust in the yawing plane. They enhance it by blowing air down the inside of the tail boom and out through a slot along it's length. Fine yaw control is achieved by installing a movable bucket on the end of the tail to direct the remainder of the air in an appropriate direction.
Back to the cliffs and the Vortex ring thread highlights how recirculation around the tip vortex causes a loss of lift which in this case would be on the side nearest the cliff. Nice theory, never seen it practice and I have hovered close to a lot of cliffs.