I measured the OLTF of both the PRM Oplev loops. Nothing odd sticks out as odd to me in this measurement - there seems to be ~40 degrees of phase margin and >10 dB gain margin for both loops, see Attachment #1. I didn't measure down to the second UGF at ~0.2 Hz (the Oplev loops are AC coupled), so there could be something funky going on there. The problem still persists - if I misalign and realign the PRM using the ifoalign scripts, the automatic engagement of Oplev loops causes the loop to oscillate. Could be that the script doesn't wait for long enough for the alignment transient to die out.
Update 1230pm: Indeed, this was due to the integrator transient. It dies away after a couple of seconds.
The PRMI Oplev servo needs some tuning, it is currently susceptible to oscillations in Pitch.