Vessbot - I get the impression you know a lot about physics but very little about helicopters.
Phase lag is governed by Lock number which is a ratio between blade inertia and aerodynamic damping.
A swash plate does not impart an instant or impulse force to a rotor, it builds gradually as a result of turning a rotating motion into a vertical one because you have to change the pitch of the blade to make it climb or descend.
No gyros I have seen have hinges that limit how much the movement of the mass of the gyro can be transmitted to the hub - a rotor system does.
Just because systems exhibit similar behaviours doesn't mean they have the same cause.