That *is* why they all us "Volt Nuts", no?
What, ME telling? O0 O0 O0
I really think, at this point, there is a natural, physical limit, where it's not useful anymore, trying to measure something, which is buried too deeply in other effects, like e.m.f.s, zener and circuit noise, etc. If you were able to have a "chopper" principle available, (like Lock-In), to cancel all e.m.f.s, and other drifts, then you would be done... but that's not the case here, as these effects are inside the circuitry.
Also, a nV meter, i.e. < 10nV noise, would dig into the 0.001ppm/K region, which makes absolutely no sense anymore.. simply look at this order of magnitude..
That has also nothing to do, that we as "amateurs" would be limited in means, compared to standards labs. I think that we are pretty close to them.
And they also are limited by the rules of physics. I really doubt, that they would give much better StD or T.C. figures for that circuitry.
I like to take the chance to present my latest measurements on a newly assembled LTZ1000 circuit, PCB and schematic by Andreas (many thanks again!!).
It's running on 45°C, the PWW resistors are selected, to give a theoretical T.C. of about +0.045ppm/K, 430k resistor for "T.C. compensation" assembled.
Measurement is done in constant environment, max. 0.8°C RT change, absolute voltage measured at NPLC 50 with the 3458A, which also was stable to 0.2 / 0.5°C, internally.
The first diagram shows the datasheet assembly, i.e. only these 3 cap's, and the LTZ in a socket. No electrical or thermal shielding, besides a styrofoam cup on top of the LTZ.
1h-noise is about 750nV, or about 0.1ppm. Not the best performer of my five new LTZs.

Second diagram shows the same LTZ, soldered fix into the PCB w/o cutting its legs. I avoided to heat the chip during soldering.
The circuit is equipped with all capacitors, as defined by Andreas, except C14, C15 (fear capacitors), and C13, which I think would spoil the ovens feedback constant of C1, R7. The metal shield is also in place, but no thermal enclosure on PCB bottom yet.

1h noise has gone down to about 270nV, or 0.04ppm. These 0.5ppm dips, and glitches were gone, at least these are much, much smaller.
So, all these capacitors, which Andreas has introduced into his circuit really improve the performance.
What's left is a random medium term noise, or drift, of about 0.05 .. 0.1 ppm, see trend line (200 points average).
That may further be improved by completing the thermal shield, and putting the whole assembly into the aluminium box.
The 16h stability, that is the combination of the 3458A and the LTZ1000 circuit, is on the order of about +/- 0.1ppm.
First conclusion, this is a quite stable measurement, mainly due to stable temperature.. it really can be done that way..
Second conclusion, despite the stable output voltage, you still see a lot of medium term noise, or variation, on the order of several 100nV.
Maybe this is caused by thermal draught, but probably also by zener instability, i.e. random walk, popcorn noise, or whatever you would like to classify this.
And I really cannot imagine, how to principally improve this, so to be able to extract changes on the order of 0.01ppm, caused by temperature variation.
Third conclusion, although there is RT change, and 3458A temperature variations, there is no correlation visible between T and U. In other measurements also, I never have seen a correlation.
Illya wonders, why he also does not see a correlation in his measurements.
Maybe, that's because there is no effect, or the effect is buried under other effects.
Well, of course, I will also try to measure the T.C., when my box will be finished.
But I will definitely stop at this 0.05 ppm/K (~100nV) perception frontier..
Andreas, I really think that 0.05ppm/K is realistic, and that all your LTZ circuits are already having that T.C. or better, by design. No need to worry further.
At a 10°C change, that would be below a 1ppm output change, which would be extraordinarily fine.
I agree, that shielding and EMI is a superior problem over the T.C. .. I also see changes on the order of ppm, depending on the configuration of the shield (outer case to ground, or using the inner shield as a guard).
Frank