BM
Actually you're completely wrong about gyroscopic prEcession. Apply an external force to a gyro (spinning bicycle wheel for example) and the effect of precession is to move the gyro as if the force had been applied at a point 90 degrees removed in the direction of rotation. So pushing the left handlebar forwards will result in bank to the left - not exactly what is required for a turn to the right.
As any cyclist / motorcyclist knows you don't move the bars to steer, you shift your c of g L or R - gyros and castor angle do the rest. However if you require an emergency fast turn to the right you initiate it by pulling the left bar towards you - it's VERY effective.
rts