I did some simulations to see if we are susceptible to HOM resonances as we reduce the CARM offset. I restricted my search to HG modes of the Carrier+[-55,-11,0,+11,+55]MHz fields with n+m<6, and used all the real physical parameters I could get ahold of. 

In short, as I change the CARM offset, I don't see any stray resonances within 2nm of zero, either in PRFPMI or DRFPMI. 

Now, the mode matching in my simulation is not the real mode matching our real interferometer has. Thus, it can't tell us how much power we may see in a given mode, but it can tell us about our susceptibility to different modes. I.e. if we were to have some power in a certain mode coming out of the IMC, or present in the vertex, we can see what it would do in the arms. 

Since my simulation has some random amounts of power in each HOM coming into the interferometer, I simply swept the CARM offset and looked for peaks in the power of each mode. Many of the fields exhibited gentle slopes over the range, and we know we ok from 3nm->~100pm, so I made the selection rule that a "peak" must be at least 10 times as big as the minimum value over the whole range, in order to see fields that really do have CARM dependence. 

In the following plots, normalized IFO power is plotted and the locations of HOM peaks are indicated with circles; their actual heights are arbitrary, since I don't know our real mode content. However, I'm not really too concerned, since all I see is some -11MHz modes between 2-3nm of full resonance, where we have no problem controlling things... Also, all of the carrier HOMs effectively co-resonate with the 00 mode, which isn't too surprising, and I didn't include these modes in the plots.

Finally, I visually inspected the traces for all of the modes, and didn't really find anything else peeking out. 

Code, plots attached.