I've just studied your other thread.
That seems to be a different story.
I think, your solution with the inner insulation is counter productive, as it rises the inner temperature too much.
The problem with all (high) precision bench meters is their T.C., which are in the same ballpark, even for the 3458A, 8508, etc.
The 3458A has an overall T.C. in its 10V range of about 0.5ppm/°C, mine has 0.45ppm/°C, lower grade ones are more like 1..2ppm/°C, both is not great.
Other 8.5 digit meters, like the Datron 1281 has probably a slightly lower T.C. 0f 0.25ppm/°C as well in the 18..28°C temperature range (oddly specified), as a lot of Vishay BMF had been used, but its direct descendants 8508A, 8588 etc. have as well a T.C. of 0.5ppm/°C, but they are not able to adapt to varying room temperatures, like the 3458A.
Mine has about 0.15 ppm/°C from the reference and 0.3ppm/°C from the A/D circuit; latter can be corrected by ACAL.
So I could reduce its reference T.C. to zero, and would be left with the 0.3ppm/°C for the A/D for the experiment run.
Therefore, high precision drift experiments well below 1ppm are not much easier, neither my regular transfer measurements of 12 sources within about 20 minutes transfer time.
Your room is not really a lab environment, isn't it?
I have a basement lab with constant temperature (+/- 0.2°C for an experiment run over 24h, +/- 2°C over the whole year), no draughts as window and door are always closed, so I don't have any problems with either the 34401A, nor with my 3458A with air draughts and I can handle the T.C. issue quite well. Over these 20minutes, the R.T. does not change more than 0.1 .. 0.2°C (caused by the operator in front of the instrument), so the drift is currently limited to max. 0.1ppm transfer uncertainty.
Concerning these fast variations you see, when you have a breeze inside your room: Do you have the handle installed?
W/o it, that would be the only way, how an outside breeze could enter the instrument and create such short termed disturbances. Otherwise, my 34401A is completely tight (handle installed), and I could not figure out, where otherwise the outside breeze could enter.
The best and only chance for you is to have a better room with mostly constant R.T. during experiments, no air draught in the lab, always monitoring the R.T, and best the inner temperature of the 34401A, as I do it with my setup and the 3458A.
Currently, I leave my 3458A always in CAL mode. If I want to make very precise absolute measurements, I make an CAL 10 against my reference bank before the experiment. Nor the 3458A neither no other DMM is a 'standard', anyway, just an adjusted scaling device with quite bad uncertainty.
So maybe you could do it the same way, if you have a reliable and "better" external reference available.
Another idea is to do RATIO measurements against a known good external reference with the usual low T.C. of about 0.02ppm/°C, so not to compromise your calibration. The 34401A also got this feature, and that would delete all such T.C. problems, additionally its uncertainty problem (35ppm/y.) using the 34401A as a scaling instrument only.
Btw.: Please try out this great RATIO function, by ignoring its mediocre and sloppy specification by HP. This is a real hidden gem, if your DUT uses as well the same 10V range, as the reference voltage on SENSE.
In this case, not the individual 24h or 365d specification applies, but the transfer specification.
For the 34401A, even latter is as well very sloppily specified.
The 3458A has 0.1ppm transfer spec, for 10 min +/- 0.5°C.
This includes both, its INL of the A/D, i.e. 0.02ppm of range plus temperature drifts over 10min.
Therefore, the RATIO function on the 3458A should give even better results, as 2 consecutive measurements are made, within a few seconds. So, you' re even left basically with the INL error of the A/D.
Same applies to the 34401A. Its INL is specified as 2+1 ppm, but my unit is
about 0.5ppm only.
Therefore, using RATIO on the 34401A might give an additional (to the reference's) uncertainty of 0.5ppm of range and practically zero T.C.
Frank