Yesterday I think I narrowed down the source of the 2 kHz frequency noise hump: it is voltage noise from the TTFSS being injected into the broadband EOM.
With the north cavity unlocked (and the TTFSS set to "test"), I monitored the (undemodulated) RAM using the auxiliary 1811 and the HP4395A. There were clear, broad 600 Hz humps on either side of the 14.75 MHz carrier. It disappeared when I unplugged the drive to the broadband EOM.
Then I looked at various test points on the TTFSS HV board with the SR785. On the COM → EOM path, the TF shaping takes the COM noise and produces (what I think is) the same 600 Hz bump, which is then sent to the EOM. In the beat, the bump appears at 2 kHz because of the north TTFSS boost; with the boost off, it reverts to 600 Hz.
This is the case on both TTFSS boards, but it only leaked into the beat on the north cavity. So I suspected it was an issue with how the EOMs are aligned on the north path. On north, the BB EOM was immediately followed by the resonant PDH EOM; on south, between the BB EOM and PDH EOM there is a PMC, an FI, and some other optics.
I moved the resonant EOM so that it follows the EOAM. After the post-EOAM PBS, I did the following:
Then I redid the mode-matching into the north cavity and measured the beat. I kept it locked for about 90 minutes and didn't see the 2 kHz hump appear, so I'm guessing this solved the issue.