And awaaaaayyyy we go again....
Lets consider at a zero wind hover to start with, and lets not worry to start with about cyclic inputs vs the direction you're trying to fly in.
At some point on the circle blade pitch angle is increased, increasing AOA.
Some contradictions in the opening statement. A zero-wind hover is (let's assume) neutral cyclic - so you won't be flying in any direction anyway. Then you want the pitch angle increased - without a cyclic or collective movement??
The usual scenario is a puff of wind, coming from ahead, affects the relative airflow. Not a pitch change.
net maximum lift at some point between the max blade pitch point and the max blade flap point
The maximum lift point, under the puff of wind scenario, (not an increase in pitch scenario) is at 90 degrees right, and the maximum flap point is straight ahead, but the extra lifting force from the puff has been decreasing as the blade rotates, to be zero effect straight ahead. But if you insist on using an increase in pitch scenario, it has to come from a cyclic movement of the swash plate, which has been feeding that extra pitch in from the tail boom right around to the 90 right, reaching the maximum pitch at 90 right, and then decreasing to zero over the nose.
BUT!! to make that happen, i.e. max pitch at 90 right, the cyclic has been pulled BACK. Not forward.
The difference between max pitch and max flap position is not always 90 degrees. In the R22 it is 72 degrees. Just the way it is. Google up Lu Zuckerman and his "missing 18 degrees". Apply a force to the blade, and as you correctly say, Mr Newton allows it to start accelerating up. To move forwards, the max pitch and max upward acceleration is at 90 LEFT, on the retreating side. The force keeps lifting the blade, but it is turning as it goes, so by the time the force is expended, the blade has turned about 90 degrees, depending on the design. The back of the disc is high, the front is low, the total rotor thrust is pointing forward, and the aircraft will respond to that force by starting to move forward.
I imagine on a hinged rotor system the angle is always 90 degrees since the hinge stop (I assume the degree of hinging or tilt is limited?!) could "damp out" the top of the sinusoid curve, or else it has to be designed to be 90 degrees or greater to stop the blade from hitting the hinge stop.
The blade should never hit its stops - the vibration will cause damage. On a B206, the blade stops are of a softer metal than the mast, so the stops will deform before the mast is damaged, or so the theory goes. The lift variations from swash plate inputs will stop the blade from flapping so far that it hits the stops and the mast.
the pressure of the blade against the hinge/tilt stop in a hinged/tilted system.
See above. In a teetering system, the disc just pulls on the rotor head through a single point, and the pendulous fuselage just dumbly follows along. This is a "zero-offset" situation - the rotor disc has no Moment to make the mast and fuselage follow the tilt of the disc.
In an articulated system, the movable blades apply the force to the fixed rotor head, and because the blades are hinged at a small distance away from the mast, a moment is generated to make the mast and fuselage follow along, making the articulated aircraft more responsive to control inputs.
In a rigid system (Bolkow/MBB/ Euroflopter) there is a virtual hinge point in the flexible blade, and it is even further out, giving a bigger moment and responsiveness. Note the Mast Moment Indicator on such aircraft to limit how much force the dopey pilot feeds in.
Many previous posts have emphasised that there are way too many variables in a rotor system for it to ever qualify as a gyroscope, but to make it easier for people to understand phase lag, it is simply stated:
"A rotor disc is LIKE a gyroscope."