I stumbled upon a faster way to stream data from the TDS3014 oscilloscopes to disk, which speeds the loss measurements up by a lot:  ftp://sprite.ssl.berkeley.edu/pub/sharris/MAVEN_LPW_Preamp/109_TDS3014B_control/tds3014b.py
This convenient(!) set of scripts contains a function that parses the scope's native binary format, for which the acquisition of 1 screenful of data takes <1s as opposed to ~20s, into readable data. I tested it for a bit and concluded that it does what it actually claims to do, but there's one weirdness: It get's the channel offset wrong. However this doesn't matter in our measurement because we're subtracting the dark level, which sees the same (wrong) offset. Other than that it seems okay.

So I started a new set of armloss measurements, and since the data acquisition is now much faster, I was able to squeeze a set of 20 individual measurements for each arm into ~30 minutes. This is the procedure I follow when I take these measurements for the XARM (symmetric under XARM <-> YARM):

1. Dither-align the interferometer with both arms locked. Freeze outputs when done.
2. Misalign ETMY + ITMY.
3. ITMY needs to be misaligned further. Moving the slider by at least +0.2 is plentiful to not have the other beam interfere with the measurement.
4. Start the script, which does the following:
   1. Resume dithering of the XARM
   2. Check XARM dither error signal rms with CDS. If they're calm enough, proceed.
   3. Freeze dithering
   4. Start a new set of averages on the scope, wait T_WAIT (5 seconds)
   5. Read data (= ASDC power and MC2 trans) from scope and save
   6. Misalign ETMX and wait 5s
   7. Read data from scope and save
   8. Repeat desired amount of times
5. Close the PSL shutter and measure the PD dark levels

I will write a more comprehensive post describing the data acquisition and processing, let's just look at the results for now: The "uncertainties" reported by the individual measurements are on the order of 1-2 ppm (~1.9 for the XARM, ~1.3 for the YARM). This accounts for fluctuations of the data read from the scope and uncertainties in mode-matching and modulation depths in the EOM. I made histograms for the 20 datapoints taken for each arm: the standard deviation of the spread is a little over 2ppm. We end up with something like:

XARM: 49.3 +/- 2.1 ppm
YARM: 20.3 +/- 2.3 ppm