I repeated the HEPA on/off test on the "low" setting several times. Here are the results.

First plot is phase noise.

Second plot is temperature noise (read with an NTC 833 atttached to each oven, AC coupled into the DAQ with an SR560).

High frequency noise seems consistently higher with HEPA on. Low frequency noise seems a tiny bit lower (factor of 2) with the HEPA on, though I don't think this really matters insofar as drawing conclusions about what the sources of noise are for us at low frequency.