In the gyroscopic precession left turning tendency, why does a pitch down cause a forward force at the top of the propeller?
The prop is a big gyro.  It's the gyroscopic precession force created at the propeller when it's subjected to an input changing its axis of rotation, where, as with any gyro, the inertial resistance to the change in axis acts at 90 degrees rotationally to the input.  

The airplane pitches down, rotating the axis (extending forward) of the propeller down, acting through the hub.  Being a gyro that is being forced to change its axis vertically, it results in precession feedback acting through the hub at 90 degrees (as if there was a thrusting force at 3 o'clock), yawing the airplane to the left.

It doesn't matter where the prop's axis is in relation to the rotational axis of the airplane in pitch, just that its axis changes as the airplane pitches.

The best way to experience it is to take off in a tail dragger with a large prop, like a Cessna 180, and force the tail up early in the takeoff run before the rudder is having any effect.  The swing to the left from propeller precession is pretty strong.