A few things that happened today:
We preamplified the gyro signal into the DAQ using an SR560 with G = 500 and found that the noise floor from the previous measurement was still there. It was slightly lower, as we were in fact within a factor of 2 or 5 of the DAQ noise, but it was there.
We discovered that the low-noise spectrum was indeed too good to be true as we were able to reproduce the noisier spectrum by increasing the gain in the AOM loop (that is, we probably had the gain set too low during the past few measurements, so that there wasn't much of a gyro signal and we were therefore only seeing phase noise).
To make sure that we were actually measuring what we want, I fed the AOM actuation signal (the other viable gyro signal candidate) into the DAQ so that we could compare it with the PLL readout signal. Remarkably, the UN-calibrated spectra for these two signals are almost smack on top of each other, which shows qualitatively that they contain the same information up to a gain factor (at least up to around a kHz, above which the AOM drive is actually quieter). The uncalibrated spectrum is below.
Upon calibrating, however, the AOM drive signal purports to be quieter in broadband. I am hesitant to believe that this is physical given how well they match up in the above figure. If it is not real, then our calibration is off on one or both of the signals. The calibration for the transmission output is the 3.09 x 10-4 (rad/s)/ct we have had from before, while for the AOM loop it is 6.103 x 10-4 V/ct * 100 kHz/V * lambda * P /(4A) = 8.225 x 10-5 (rad/s)/ct. Here is the calibrated spectrum.
Either way, BOTH of these spectra are way too noisy. What I suspect is happening is that there is residual noise that is not canceled by the CCW loop that spills over into the CW servo. This is another way in which displacement noise can directly couple into the gyro signal. I will get with Rich tomorrow about the PDs.