OK Lu let's start again.
1. Assume that the pitch operating arms are mounted to change the pitch of the blade exactly matching the tilt of the swashplate (no advance angle).
2. Assume that the swashplate tilts in the same direction as the cyclic is moved.
3. Use the same 18 degree collective pitch setting as you did.
4. Push the cyclic forward to set the same pitch settings as you had = 18 degrees at 3:00 and 9:00, 24 degrees at 6:00 and 18 degrees at 12:00.
Happy so far?
5. Start with a blade at 3:00 - as it moves towards 12:00 it sees a change in cyclic pitch that reduces tha AoA so the blade loses lift and begins to flap down.
6. At 12:00 it sees the minimum cyclic pitch setting and so has the least lift - it cannot start to flap up as it has 6 degrees less pitch than when it started to flap down. Therefore it continues to flap down past the 12:00 BUT at a reducing rate because the cyclic pitch is increasing back towards the neutral 18 degree setting at 9:00. THE BLADE IS AT IT'S LOWEST POINT AT 9:00 DUE TO PHASE LAG.
7. For the remaining 180 degrees the opposite happens and this is why maximum/minimum cyclic pitch must be applied 90 degrees before the desired blade high/low point. This is achieved by tilting the swashplate and/or mounting the pitch operating arms ahead of the blade feathering axis. THIS IS NOT A MYTH AND ALL HELICOPTERS (except oddballs like the one you described) USE VARIATIONS OF THIS IDEA.
8. The phase lag is only truly 90 degrees on a teetering head rotor system and the figure reduces as the flapping hinge is moved outboard (hinge offset).
The rate of cyclic pitch change is not constant although the rate of angular displacement is :
Draw a clock face with a horizontal line underneath it so 6:00 is touching the line. Draw vertical lines down from 1:00, 2:00, 3:00 and 4:00 to the horizontal line. From 12:00 to 1:00 is 30 degrees and so is 1:00 to 2:00 and 2:00 to 3:00 and 3:00 to 4:00. This is constant angular displacement.
Now look at the distances between each of the vertical lines where they cross the horizontal line - they are not equal. The distance between 12:00 and 1:00 is greater than 1:00 to 2:00 which is greater than 2:00 to 3:00. The pitch change arm moves up and down at different amounts depending on which 30 degree segment of the circle it is in and if plotted would produce a perfect sine wave.
On a swashplate system (known as a control orbit) the maximum rate of pitch change occurs during the 30 degrees arc either side of the maximum/minimum pitch setting which is surely proof enough that the blade cannot start to flap up again at 12:00 in the above example.
The only time the precession causes the 90 degree phase change is in a theoretical model of a rotor system in a vacuum where aerodynamic forces are completely discounted. This model is used to illustrate what subsequently happens when aerodynamic forces are introduced - ie the real world and not theoretical physics. The 2 effects have the same end state but only the aerodynamic effects are generally considered since we don't fly helicopters in space!
Please read this carefully Lu and then go and read Prouty/Padfield/Gessow and Myers. Then come back and tell me if anything they say is different to the above (it's not).
Or.. look at a helicopter rotor head and examine carefully where the swash plate tilts when you move the cyclic and also how far angularly displaced ahead of the blade are the pitch operating arms.
Sorry to go on but this does need sorting.
If you still disagree then I will e-mail you extracts from appropriate publications to show I am not making this up or blindly quoting Brit-Mil dogma.