Wing pitching moment decomposition into two terms
Interestingly, when $O=AC$ and $x_O=x_{AC}$, the moment does not change with changing $α$


Yes, but only if your lift is also applied at the AC! That's the whole point of the aerodynamic center. You replace the pressure distribution with a lift force (actually a resultant force, but let's neglect drag here) and a moment. If you place the lift force at the center of pressure, then the resultant moment about that point is zero. Then, the moment about any other point $O$ is only "created" by the resultant force. So in that case indeed: 
$$M_O = (x_{CP} - x_O)L$$

If you now place the lift at your AC and also O=AC, then:

$$M_O = M_{AC}$$

This $M_{AC}$ is independent of $\alpha$. If you now move to any different O, you get:
$$M_O = M_{AC} + L (x_O - x_{AC})$$

The first term $M_{AC}$ is what you are calling "$M_{camber}$" and the second term is your "$M_{lift}$".