Using the same sample as I was using yesterday (the 20mA run), I am seeing the same stable point as Alex for the Zener alone... 1.4mA, 5.251V. This appears to be another turnover point: Negative TC below, Positive TC above. My sample seems to hold within about 20uV over a range between 20-24'C.
I guess the two turnover points make some kind of sense, the higher the current the more positive the TC of the zener becomes until it matches the negative TC of the diode, but not until about 20mA. Much higher than the expected 5 - 7.5mA. Below 20mA it seems that the positive TC slope of the zener is too low. [Edit:] I'm assuming that the TC of the diode will remain pretty much -0.6mV/'C regardless of current.
A solution (if achieving lower noise than at 1.4mA operation is a priority) may be to add a divided down portion of the diode forward drop to the zener voltage. Maybe this could be done by biasing the diode separately and using passive divider?
One other thing. Has anyone else noticed that the leads seem to be made of rather stiff grade magnetic steel? I've avoided risking my good cutters on them but even my carbide ones take a bit of force. There also seems to be a bit of crazing on the glass to metal seals of most samples, possibly due to the lead length and stiffness. I think they will need mounting with care to avoid stresses.