....I bought one of those reference modules off ebay that uses the AD584LH chip (5ppm). I know this machine has not been NIST traceable for at least 5 years, probably longer, and it was 10 counts high compared to my reference that is claimed to be checked against a NIST traceable 3458A. Probably nothing to worry about but I want it to be spot on to my best known reference even if it is slightly off.
I am a hard core perfectionist and the little details matter to me.
If you are a perfectionist, I recommend you to first learn about the basics of metrology.
Obviously, you confuse temperature coefficient of the AD584L (i.e. 5ppm/K) with the uncertainty - measured in a different unit, namely ppm - of the assembly from ebay, and the uncertainty / stability of your 3456A, which is 8ppm/24h or 23ppm/90days .
If the room temperature, where you now operate your AD548L, deviates only 2°C from the calibration temperature, the output will deviate already by 10ppm, that's what you observe already.
To calibrate the 3456A, you need a reference, which is uncertain to 1ppm relative to NIST, and has a T.C. of < 0.1ppm/K.
I have seen descriptions of those chinese 4-channel references based on an AD584L, but the uncertainty (again: in ppm) is to my knowledge not defined at all.
They show photos with a 34401A only, and that instrument - IF freshly calibrated - is uncertain to 20ppm only.
Even if they would calibrate it against a 3458A, the AD548L is way too unstable (over temperature and time) to make a useful reference for calibration of 6.5 digits DMMs.
A reference for the 10V range alone also is not sufficient to calibrate that instrument, for DCV only you need those 5 Cardinal Points: 1000V, 100V, 10V, 1V, 0.1V.
Better trust the 3456A as is.
Frank