The lower crown in this case will not move.
That is the whole reason for AP having to cut head tube.
The upper crown is obviously maxxed out too.
The stack height needs to fit in-between.

No magically levitating, just cutting metal to make it fit.
All I'm saying is that the location of where the cut is made can have an effect, and that effect can, in fact be controlled by making the cut on the bottom side or by splitting the ammount of materiel by making 2 smaller cuts, 1 on top and bottom.
This way, the geometry can be slightly manipulated.
Cutting the bottom of the frame head tube just moves the lowest point on the stack to where it fits.
Cutting the materiel from the top of the head tube effectively lowers the top point on the stack in relation to the rest of the frame.

When re-assembling the bike, there will be a slight difference in head angle if the cut is made on the top side of the head tube.