To estimate the RAM before the measurement, we can use the following logic:
The cavity has a linewidth of ~100 kHz. According to the Gyro Doc the gyro signal df ~ omega / lambda, where omega is the rotation rate. Since the noise now is ~10^-5 rad/s, this is equivalent to ~10 Hz/rHz of frequency noise at 0.1 Hz.
This would require a AM/PM ratio of ~(10 Hz / 100 kHz) ~10^-4 at 0.1 Hz. Its easily possible; I have seen things of this size.
Another possibility is that our setup has been made especially sensitive to this by the PBS after the modulator. The RAM typically gets made by unwanted polarization rotation. If we have tuned a waveplate to split the power after the EOM 50/50, it means that we are also in the configuration where the polarization -> AM conversion is maximized. We can reduce this by trying to do a polarization insensitive split or by having separate EOMs in the two paths.
To verify that its a polarization to AM conversion, you ought to adjust the waveplate to put minimize the power in one path and measure the RAM in the other one. Then you ought to be quadratically sensitive to the angle.