I think it shhhoouulldd be relatively simple to drop in a vreg set to 6.3V, but I just want to get someone more knowledgeable to make sure there's not a trick hiding in there.
Hello,
before LM399 the 1N829A zeners were state of the art for up to 6.5 digit instruments.
These zeners are selected for T.C. (zero T.C. current) and usually also for noise.
Typical you have around 2-3 uVpp with these so you cannot replace them by a standard
bandgap (like TL431) which has minimum a factor 5 more noise.
I also guess that R1 (resistor array) is specially paired/selected (with low T.C.)
together with the zener to get accurate output.
So it will be difficult to use a standard voltage divider (with 50-100ppm/K T.C.)
without degrading the cirquit.
1N829A are still available (e.g. at Farnell) even if they have now much higher price
as they used to be at the time when they were state of the art.
Eventually you will have to adapt the 1K resistor to get optimum
zero T.C. current for a different device.
So before replacing the temperature compensated zener with
a different device I would carefully check if I can maintain the specs
of the instrument with a different (low noise, low drift) voltage regulator.
With best regards
Andreas