TL;DR we were previously underestimating the coupling mechanism of radiation-pressure based intensity to DARM by a factor of 2.  This was causing us to inflate the arm power difference by a factor of 2.  Work on understanding this in the context of the SRCL dither measurement method is underway.

While writing up the math for radiation pressure intensity coupling to DARM, I made the derivation in PDF attachment 2.  
This was a factor of 2 greater than what was previously used (alog 46683).  Thanks to Gabriele for helpful chats and models about this.

I tested this equation in the LHO finesse model Dan and I have cooked up to model the DARM plant.  
If I correctly include both ITMs and ETMs in the RIN to DARM response [i.e. DARM = Lx - Ly = (Ex - Ix) - (Ey - Iy)], I get good agreement between the finesse model and the analytic model (within 5%).  This sort of verifies that both models are telling us the same thing.

For the actual LHO input RIN to DARM measurement, if I fit the analytic model to it between 20 and 50 Hz, I find deltaP = Px - Py ~ -8.6 kilowatts.  
This is shown in PDF 1 with the measurement = blue, and analytic model = green.

deltaP is the one number this measurement can really nail down.  The following is additional info/speculation.  

- I have not gotten to including contrast defect in the finesse model or the analytic model.  This starts to dominate at 100 Hz, and can affect the overall magnitude before this.

- We at Hanford expect a finesse difference in our arms of 5.5% due to the transmission of the ITMs (T_ITMX = 1.50%, T_ITMY = 1.42%)

- Power parameters at the time of the measurement:
Pin on back of PRM = 32.8 watts
PRG = 43.9

- Running our LHO finesse model produces the following (plotted as orange in PDF 1):
Finesse Arm Powers
Px = 182046 watts
Py = 192348 watts
deltaP = -10301 watts
Pavg = 187197 watts
deltaP/Pavg = -5.5%

- The analytic fit deltaP ~ -8.6 kilowatts suggests a 4.6% arm power imbalance for an average arm power of around 187 kW as suggested by finesse.

- script in /ligo/home/craig.cahillane/Git/IFO/IntensityNoise/scripts/intensity_injection_meas_vs_finesse.py