Thank you for the summary.
I think now you are getting into a phase where you should start doing some quantitative and careful checks.
1. Calculate how much light will be reflected from the cavity if the alignment is perfect.
2. Investigate where those kHz oscillations are coming from.
3. Estimate how much the 1.1 kHz corner frequency in LPF will reduce the phase margin around 10 kHz.
4. Calculate the estimated amplitude of the PDH signal.
5. Compute how big the gain of the PDH box should be.
This is a kind of summary of what I have worked on this week.