If I understand NorthSouth's account correctly, the aircraft pitches down whether the yaw is left or right. That means that it can't be a gyroscopic effect.
It would be interesting to know if the effect depends on sideslip angle or really on yaw rate. Does it pitch down (more than you would otherwise expect) if you hold it in a slip?
(BTW any reason why you didn't put this on Tech Log? Lots of expertise here, I'm sure, but aerodynamics seems to be a strength on Tech Log)