Just looking at the aerodynamic forces one would expect a 180 degree phase lag, because the upwards movement needs to be slowed down first by downward forces.
Or in fact by a reduction in the upward force due to the reduction in pitch angle and AoA as explained earlier and the reason it is around the 90 degree mark.
And you have completely forgotten the periodic drag changes as the blade spins round (the reason rotors have drag hinges or dampers)- something a gyro doesn't have - there are more differences than similarities between a rotor and a gyro but you can't seem to see past the spinning bit. Each blade speeds up and slows down in its journey because as CL increases due to increase in AoA, so does CD (coefficients of lift and drag respectively).
What would a gyro do if you sped it up on one side? It can't because it would speed up the other side too - unlike a rotor.