I checked the CC PLL fast and slow control as described in 1205, with the only difference being that I used 21 MHz as the base signal. The purpose is to see how the PLL control loop responds to small modulations in a beat signal that is somewhat offset from the main LO.

For 1 MHz deviation, I saw DC offset ~ 50 mV (vs 10V for Yuhang) and no apparent AC signal. (fig 1)
For 1 kHz deviation, I saw DC offset ~ 50 mV and a somewhat messy signal with several frequency components. One is about 1.7 kHz (fig 2) and 100 Hz is highlighted in figure 3.

Seems like the fast loop is behaving a bit strangely

I also stared at the fast and slow loop oscilloscope signal for a few minutes each but didn't see much glitch behaviour. Probably not a conclusive test though.