Dave,
There is no remaining 18 degrees. The rotor flaps so that it is exactly in tune with the pilot's cyclic input, and this is because it moves in concert with the lesser phase angle.
Let me use an analogy. You are always shooting a 30 cal rifle with a 180 grain slug that travels at 3000 feet per second. When you shoot you aim 3 inches high at 100 yards. Everybody always said that they aim 3 inches high at 100 yards. The books said that all rifles require that you aim 3 inches high at 100 yards. We call that normal, it is taught in all the books, and it is gospel.
Somebody comes along with a rifle that shoots a faster bullet, which only needs 1 inch of elevation at 100 yards.
Where did that lost 2 inches go?
If the rotor flaps faster, the flap occurs sooner in the rotation, so the rotor phase needs fewer leading degrees. Is this really that complex??