I tried to gather more information about the wandering peak in the F1 LVDT readout. However, I couldn't find much more than what it's been reported already
The screenshot shows the amplitude spectral density (ASD) in linear scale of the free swing readout of the three GAS filter LVDTs. The plot in blue corresponds to the F1 LVDT. In this screenshot, the wandering peak is at 20 Hz. During a couple of hours, the peak moved between 6 and 46 Hz (indicated by the blue vertical lines). It did not move in an uniform way, but erratically. Besides the wandering peak, there is a fixed peak at 33.5 Hz that appears and dissapears, maybe by hours at the time.
I measured the ASDs of all the other GAS filter LVDTs in Type-B suspensions, but none of them showed a wandering peak. The feature that distinguishes the F1 LVDT is a stray connection to the chamber. As suggested by Aso-san (entry 18964), we could measure the voltage of the chamber with respect to ground and search for a correlation. Another strategy would be to connect the chamber directly to electrical ground (as we have assumed it is) and see whether the noise dissapears. The second option seems easier.