I have just borrowed a 1 GHz InGaAs and HP spectrum analyzer from the 40 m.  While I was doing some other things I have set one cavity to lock and the other path's laser on a ~1 mHz temp ramp with the spectrum analyzer on max hold.  Its still doubtful this will catch a beat note.

I will configure pick off from both paths so at least we can know that we are within the bandwidth of the detector without having to deal with the tiny frequency windows of transmission of the two reference cavities.

You make a good point of figuring out the appropriate heating needed, at least we will know if we are even in the ballpark of getting a beat note.