Regarding..
However once the variation of AoA comes to an end and the AoA remains constant, all the lift takes effectively place at the CP. So the pitching moment must change and generate a pitch up or down (depending on the position of the CG compared to that of the CP).
Perhaps I missunderstand what you are saying but that's not correct. The pitching moment doesn't change just because the AOA stops changing.
I think this bit..
the lift (L) is effectively applied at the center of pressure (CP, which position changes for different AoA) while the change in lift (Delta L) takes place at the AC
might be confusing you.
A wing generates forces and torques. Neither ever act at or about a single point. For example the lift force is allways distributed over the surface of the wing. To some extent the AC and CP are just mathamatical constructs that make the maths easier. They don't change anything in the real world any more than changing from Cartesian (xyz) to Polar (r, θ) cordinates does.
For example lets say you want to write one equation for the vertical forces acting on a wing and another for the torques. If you choose the leading Edge as the origin then both equations feature the AOA. If you choose the AC as the origin only the one for the vertical forces features the AOA. In effect you have simplified the equations without having to do extra mathematical steps. However nothing has changed in the real world so you would get the same answers eventually.
So for the purposes of this thread.. If the AOA stops changing then the pitching moment also stops changing.