The aircraft will rotate EXACTLY at the CG.
As a side note, the CG will actually lose a little altitude until it stabilizes
at the new attitude.


I think this absolutely has to be the case.

CL is simply the place the overall lift averages out to. It's a FORCE
acting on a body. And so is any force acting on the horizontal tail
surfaces, or acting on any other place on the plane.

The body has a CG and it will rotate at the CG.

Displacement is another matter.