This measurement tells you how the gain balance between the SLOW_CM and AO paths should be. Basically, what you need is to adjust the overall gain before the branch of the paths.

Except for the presence of the additional pole-zero in the optical gain because of the power recycling.

You have compensated this with a filter (z=120Hz, p=5kHz) for the CM path. However, AO path still don't know about it. Does this change the behavior of the cross over?

If the servo is not unconditionally stable when the AO gain is set low, can we just turn on the AO path at the nominal gain? This causes some glitch but if the servo is stable, you have a chance to recover the CARM control before everything explodes, maybe?