It's taken a lot of trial and error, but I've found a path through MATLAB loops that seems like it may be stable at all points.
CAVEAT: This doesn't give any indication as to why we weren't able to turn up the AO gain more last night, as far as I can tell, so it's not all good news.
However, it's still ok to at least have a plan that works in simulation...
Based on the location of the optical resonance peak in the CARM plant, we estimate our CARM offset to be 200pm. I haven't simulated TFs there exactly, but do have 100pm and 300pm TFs. This procedure works in MATLAB starting at either, though 100pm is a little nicer than 300. MATLAB data and code is attached in a zip.
The steps below correspond to the attached figures: Bode plots and step response of the Loop at each step.
0. [Not Plotted] DCTrans sensing, MCL actuation on CARM. FMs1,2,3,5,8; UGF = 120. (DARM not considered at all)
#4 Seems like the most sticky part. While both sides of this look stable as far as I can tell. I feel that flipping from the red phase curve to the teal might not actually be ok, since they are on either side of the bad phase of 0 degrees. It isn't immediately evident to me how to easily model the transitions between steps, rather than just the stability of of each step in the steady state.