The explanations about blade path length etc are aerodynamic factors.
Gyroscopic effect is just about the heavy prop acting as a big gyro. So ignore
anything to do with thrust. This is just gyro precession.
So, big gyro on the nose going round clockwise. Pitching up means you are trying to tip the gyro up
by pushing on the bottom. Precession means it reacts as though you were pushing
90deg round in the direction of rotation, that is on
the left edge, so the effect is to yaw the aircraft right.
Similarly, right yaw is trying to push the big gyro round to the right,
pushing on the left edge, but precession makes it act as though the force were
applied to the top of the gyro, which gives pitch down.