Jon,
We got the LM399AH and LTZ1000 from Mouser awhile back, when the LM399AH recently came back in stock we got another couple LM399AHs.
These were used in a couple custom reference designs shown. They are based on the bootstrap method for both the LM & LTZ references, and powered by 24V and use a 15V regulator to the heater and op-amp. The cases are 3D printed, and the dark blue holds a LTZ1000, LM399AH and another 10V reference (can't remember which one). The lighter blue holds a LM399AH and a 10 volt reference (can't remember which one), and also has a 1V and 0.1V output based upon a 10X type 9 resistor precision voltage divider (3 series and 3 parallel) and CAZ op-amps. We keep these running 24/7 from a cheap eBay 24V SMPS (one LM399AH has ~10,000 hours, the LTZ and another have ~500 hours), and when making a measurement we use a linear supply for the 24V input.
BTW you are going really enjoy the KS34465A, these are the older brothers of the famous 34401As. You can even get a 7 digit result using the MX+B function
I believe (no evidence tho) these are the same hardware as the 7 1/2 digit KS34470A with exception to the reference, which is the LM399AH in the 65A and LTZ1000 in the 70A. Maybe someone in the "know" will comment
With your skills you could roll your own 10V reference based upon the bootstrap technique.
Edit: It's seems you could modify the design you've shown to a bootstrap type by moving the 5.6K resistor to the op-amp output and changing it to a 3K. You may need a high value (~200K) startup resistor to the supply rail if the LM399 reference doesn't start.
Edit: Here's some schematics & 3D models for the custom references.
Best,