Thanks for the great advice Dr. Frank and TiN.
I wish I had a basement, but that's just a dream for us apartment dwellers.
I would not even dream of powering the references with a switched mode PSU! They are powered from my Thurlby PL320 linear supply:
I think I have a suitable metal tin to create a shielded environment for the reference and I should also be able to fit some LiPo battery packs in there to provide power for it. That will go a long way towards removing RFI influences. I just need to get some more screened PTFE cable as I seem to have run out.
I let the log continue running and got one huge -80ppm jump last night as shown in the plot below:
When that happened, I took my wireless environmental monitor and relocated it to the other side of the room. This forced me to restart my logging script as the subtask which adds the data from the sensor stopped updating when I had to unplug the sensor to move it. It is interesting to see what happened to the 34401A's readings after I restarted the script. If you look at the plot just after the -80ppm spike, there's a change in the logged voltage back to the 0ppm difference level when I restarted the script (which starts with a *RST command).
It looks like there was something causing an offset to the readings which got cleared when I reset the meter. By default, the 34401A should be performing an auto zero on every reading with the settings I am using, so either that's not true (and I will change the script to turn on auto zero explicitly), or there's some other offset source accumulating in the meter which isn't accounted for by the auto zero.
I hope it is caused by auto zero not being on by default. If it's not, and there's some other kind of offset building up over time, it kind of shakes my confidence in the 34401A for long term logging.