This morning I've inserted (in the guard state of the LowNoise2) the reduction of the 6MHz modulation index as suggested by Alain from the 0 to the -15 dB (during the lock acquisition is at 15db).

In order to do that the MICH error signal normalization has been moved from 12MHz to 112MHz (measuring the TF between the two signals and compensating in the loop gain).

The comparison between  the usual 6MHz modulation index (0) and the new one (-15) is shown in Figure 1 (old = purple, new = blue).

To be checked if this level is low enough to kill the beat with the 8MHz and the associated non linearities (it would be nice to leave even if it small a bit of 6MHz to better characterize the ITF).