Cool! He seems to discuss thermal vibration transmitted through atoms of gas, photons, and thermal contact through the fiber. However, he doesn't seem to discuss non-thermal sources of vibration. Hasn't he simply designed the world's most sensitive seismometer? These vibrations aren't thermal in nature, and can't be eliminated by cooling. I don't understand the last section of paragraph II, which seems to be addressing something related to this. The first two sentences don't seem to be connected logically to the rest of the paragraph.
This seems very similar to what LIGO does, but they're still measuring displacements many, many orders of magnitude above the Planck scale. I guess the big difference is that Bekenstein's design involves time intervals that are short (e.g., compared to the time between hits by atoms of gas), whereas LIGO uses time intervals that are long, so they're in the business of averaging out the thermal fluctuations.
In his discussion of vacuum, he says that He is what you'd choose to use, because the low mass is more favorable. But when you're trying to achieve high vacuum, you don't necessarily get to choose what gas it is you're pumping out. Different types of vacuum pumps work differently (e.g., cryopumps get rid of stuff that condenses, turbopumps work on everything). I've never worked with high vacuum at this level, and I don't know what techniques they use. But I suspect that you might be dealing with a lot of high-molecular-mass gunk such as finger grease or stuff that outgasses from various surfaces, which also might be high in molecular mass.