I don't think the effect of airflow on the horizontal stabiliser has yet been mentioned.
I was taught that when the engine quits, reduced lift due to lowering the lever and low RPM causes descent and hence upward force on the rear stabiliser which causes a nose down attitude.
For memory, the small lip along the top of the leading edge of the B206 horizontal stabilizer was there to stall it in autorotation and reduce that tendency.
Would be interested if anyone can confirm that.