Thanks to Andreas here is a 24h + x measurement taken with Keysight 3458A at 100NPLC of my may years running LM399.
There is some related drift, but I can't say if this is due to a change of temperature in the controlled lab, if it is drift by the reference itself or if it is due to the drastical change in weather from yesterday morning (calm) til this morning (stormy with 80km/h) and thus a change in ambient pressure. The ambient monitoring system is currently in use in another lab

However, after removing the drift component by a parabolic function the mean is 10.0017577V with a standard deviation of 1µV. My reference obviosly shows popcorn noise in the order of ~3µV.
I plotted Allan Variance before and after removing the drift component... need help to interprete the charts. I attached the original data, so maybe someone wants to analyse them and give some feedback?
EDIT:
Removed reference and added a short at the input of the 3458A, to see how noise compares in this situation. After a small thermal settling time of the short the noise is only a few hundred nV (still 100NPLC @10V). So the popcorn is proven to be from my LM399. Seems it's time to activate my LTZ and take some 24h hour measurements.