Interesting, so it does seem to be related to the start of dissymmetry of lift. It’s surprising that it causes such a big change, but I guess it makes sense. We are moving out of a near vertical induced flow of air to a relatively undisturbed horizontal flow of air. The AoA change on the advancing side is probably quite dramatic.
Ahh, now you are getting into Translational Lift, which as you correctly say, is moving into air that has had little chance to start moving downwards through the disc. And push it down you must, in order to hold the aircraft up. A lot of theory books concentrate on the Bernouilli equation without mentioning that the airflow at the back of the airfoil is headed downwards - the flow over the top doesn't "have to meet the flow underneath", and in fact it gets there well before the lower flow, hence the movement downwards, the downwash.
The term Gyroscopic Precession has used up many threads on this site. It is only a means of understanding the dynamics of the rotor system, but the rotor is NOT a gyroscope. Phase Lag is the correct term, and it is fixed by adding an Advance Angle to the inputs from the swash plate to the disc. The lag is approximately 90 degrees, but gets as low as 72 degrees on the Robinson. But if precession is the way to grasp this concept, go for it, but don't tell anybody that you believe in it. A bit like being a Flat Earther.
Regarding Dissymmetry of Lift, it only happens until the pilot pokes the cyclic forward to stop the flapback. After that the lift on both sides is exactly the same, in steady flight. The retreating blade is suffering, with the relative airflow reduced by the forward velocity, so the advancing blade has to "throw away" all that beautiful lift it gains from forward movement, to match the poor cousin on the other side.