I don't understand. Why would the blades move at all? They're in a vacuum. There's no lift to cause displacement. Pitch/AOA would have no effect.
Since there is no aero force, the pitchrods will follow the swash plate uphill and down, altering the pitch of the blades but also pulling them down and pushing them up a little - no phase lag and no precession. Even with your central pushrods, the blades will rise and fall but follow the swash plate exactly.
Completely untrue, consider the spacecraft in orbit. 90 degree phase lag.
not phase lag - might well be precession though.
Now you're presenting that "the shaft axis is the rotors spin axis" as a necessary feature of gyros that separates them from rotors. But this isn't a difference either, because it's false. See the cardboard on the pencil gyro video, where the spin axis was displaced from the shaft axis. Like a rotor.
The pencil with the cardboard disc isn't attached to the disc nor is it providing the drive to keep the disc spinning - it is simply a support to stop the disc falling to the ground so that is a false argument. A gyro's spin and shaft axis remain aligned throughout its movement and precession. The apparent spin axis of a rotor is displaced from the shaft axis of a rotor when the disc flaps.
I think this is what happens when you have knowledge as a collection of facts, rather than understanding as the inference from particular facts to a general principle, and then application of the general principle to some other particular thing in question.
And you took me to task for talking down to people...........