Dave,
I am responding to your first assertion, that phase angle and delta three are not related. You wrote: "In addition, I can see no reason why the delta-3 angle and the reduction in the phase angle need be the same, other than that of keeping the pitch link vertical."
As I have tried to say, the delta three will change the phase angle, so if you took a hypothetical helicopter, with the proper phase angle, and then modified the head with some degrees of positive delta three, you would discover that the phase angle was now wrong by exactly that number of degrees.
This is a simple fact of head geometry, as I have tried to state. Both you and Lu seem to think otherwise, and you are not correct.
When we added the delta three to the S-76, we had to change the mixing to account for the different phase angle. Most 76 pilots know about the "analog beam phase shifter" on the upper deck, which was added to get gamma back to the right setting.
You are correct, however, in that the delta three can be used to straighten out the cyclic, as positive delta three will make the cyclic go to the right with speed, so if is was going to the left, some delta three would straighten it out. Seems like a complex way to do it, however. The angle of the cyclic stick travel would also be exactly the delta three angle.