I've really enjoyed these volt-nut threads and though I'm a newb, I've started down my own path of designing an LM399 reference.
The idea I'm exploring is to avoid any sort of trim on the output op-amp's voltage divider (just two fixed value resistors to set the gain). Rather, I'll achieve trim by adjusting the current driven through the LM399 zener.
Not only that, but I'll control the current source for the LM399 zener via a DAC, so that you can calibrate it via software. This means I can immerse the entire circuit in an oil bath and not have to crack it open while calibrating to tweak a pot, etc.
So, the first step down this path is coming up with a current source.
My first attempts were a traditional op-amp with current sense resistor on the low side. However, I realized having the current sense resistor on the low side would introduce current error one way or another.
So I tried wrapping my brain around making a high-side current source, and this is what I came up with:
(Here, the DAC is represented by a voltage divider, and its reference represented by a simple zener).
Using this setup, a drift in the LM317 of +/- 0.1V results in a current source error of only 2.3 uA. Not bad!
I'm initially choosing an LM317 target of 16.25V (using R values of 100 and 1200), as that allows operation from three 9V batteries discharged down to about 6.5V each. (the batteries would be needed while e.g. putting the reference in a faraday cage -- I have terrible noise pickup at my house).