I made some measurements to try and see if any difference could be seen with different CARM offset signs.
Specifically, at various offsets, I used a spare DAC channel to drive IN1 of the CM board, as an "AO Exciter." I used CM_SLOW to monitor the signal that was actually on the board. I used the CARM_IN1 error signal to see how the optical plant responded to the AO excitation. Rather than a swept sine, I used a noise injection kind of TF measurement.
Here are plots of CARM_IN1 / CM_SLOW at different CARM FM offsets; I chose to plot this in an attempt to divide out some of the common things like AA and delays and make the detuned CARM pole more evident). The offsets chosen correspond roughly to powers of 2, 2.5, and 3. I tried to go higher than that, but didn't remain locked for long enough to measure the TF.
By eye, I don't see much of a difference. We can zpk fit the data, and see what happens.