I've extended my analysis to the PRFPMI case, with the current working knowledge of radii of curvature and cavity lengths. However, losses were not included.

I do not see any HOM activity within about 20nm of the carrier TM00 resonance. 

Basically, what I did was use the standard formulae for the reflection and transmission coefficients of FB cavities viewed as compound mirrors. However, I modified the normal spatial propagation terms to include the additional Guoy phase accumulated by the HOMs. I created these coefficients for each arm individually, and then used (rX + rY)/2 as a mirror in the PRC, and used that to create the transmission coefficient for the PRFPMI as a whole, as a function of frequency offset from the carrier, spatial mode order and CARM offset. As a check, this produced the correct finesse for the carrier lock to the single arm and PRFPMI. 

Here is a PRFPMI CARM FSR of all of the fields' power transmission coefficients, up to order n+m=5. 

One can observe some split peaks. There are two causes, the biggest effect is the mismatch between ETM radii of curvatures (ETMX:59.48, ETMY:60.26):, followed by asymmetric arm length(X:37.79, Y:37.81). (I judged this by the visual change of the plot when changing different factors). 

In the following plot, I broke down the peaks by mode order:

Code, plots attached!