Dave,
I think you tend to explain things backwards - not wrong, but rather mixing cause and effect. Let me try to straighten things out:
The rotor of a helicopter does not tilt exactly as the cyclic moves, in virtually any case, it moves a few degrees off, depending on a raft of factors. That is documented in many posts on this site. Most helos have a bunch of mixing of long and lat cyclic in an attempt to make the stick feel close to correct. It mostly works. We call that mixing "phase angle" adjustment, and we tell newbies it is for "gyroscopic precession." That fiction works, and most of us sleep at night as a result.
On top of that, we sometimes mix in some delta three, where the flap hinge is not aligned with the pitch horn, so as the blade flaps, it reduces (or increases) blade feathering pitch. Positive delta three makes the blade feather less. Delta three is put in so that the blade delivers less force to the head due to outside disturbences, such as gusts. It acts like automatic cyclic stability, so it is often used to smooth out rotor response to gusts (makes a more stable helicopter). It is also good at making a tail rotor withstand the speed differences between a hover and Vne, so lots of delta three is used on tail rotors.
The angle of delta three is simply the angle between the flap hinge and the blade pitch change horn, relative to the tangent to the rotational axis at the flap hinge location. For a horn that is in front of the flap hinge, if that horn were farther out in raduis from the flap hinge, the delta three would be positive, in that an up flap (caused by an increase in lift) would cause a reduction in blade pitch (and a reduction in the blade lift).
One real effect of delta three is to make the blade flap about a new axis that is not perpendicular to the radius. With delta three, the phase angle is screwed up, so we must adjust it exactly one degree per degree of delta three. Why? The blade actually rises earlier with positive delta three, so it needs less phase angle. The S-76 has 17 degrees of delta three (added for gust alleviation) so the mixing angle is 17 degrees less. This makes the cyclic feel correct, and that the nose goes down with forward stick.
Lu used to think the geometry of the Robinson head made the cyclic behave differently, because he did not understand the delta three correction, I think he has changed since then, but he can tell you that.
Now for your conclusions, delta three does soften out cyclic so we need more cyclic range to get the same control. This is not all bad, but the head geometry must be designed with this in mind. Delta three softens out the aircraft's response to gusts, so it acts like a stability augmentation system, a powerful one.
Delta three does make a change in gamma (phase angle0 and must be accounted for in the rotor design, or else the cyclic will feel funny, in that forward will produce some roll.
The cyclic plots you show are quite representative of common helos, but don't think that the rotor head is the only way that moments are produced. The lateral stick shift can be a product of the delta three (its angle is the reason why the first plot moves off to the right) but it also follows the lateral balance of the aircraft, which can be changes thru CG or through the horizontal tail. A left side tail will produce a strong download at speed, and require some right stick to balance (and vice-versa).