Ok, installed fresh resistors from a reputable vendor, went fine, even the exercise is not for fainthearted makers..

After an initial cleanup I fired up the meter - see below - and let it run overnight. The initial warmup looks pretty different compared to above LM399#7 and preliminary wiring. Below some data.
Note: the meter's 10V range has not been adjusted against my ADR1001#1 yet so it does not show the "proper 9.999896V" but 10.120.505 because the ADR1399#1's voltage is way lower than the HP399's one.
Because of kind of weird results I stopped the measurement this morning and double checked the voltages - ADR1399#1 shows 6.921V and all the other voltages look ok as well.
Now - the issues - the 6.921V creates 10.120500V against my ADR1001#1 reference, so the resolution is 1uV via serial (all my measurements before were below 10V with the "additional 7th digit"), the +5REF is now much lower as well.
The STD below is way much higher (one would say "all over the place") than with any previous 399s, also see the missing code in the TC plot.. With higher internal temperature the STD increases. So we have to investigate..

Note:
- the TC plot below is against the internal dmm temperature during the warmup
- 10NPLC against ADR1001#1
- STD over sliding 100samples (40secs)
- the 47k (RN73R1JTTD4702F10CT-ND) and 820 ohm (RN73R2BTTD8200F10CT-ND) resistors are [should be] 10ppm/C thin film one (digikey), the snubber's R is a piece of manganin wire with aprox 6ohm
- I also replaced one zener dropper in +15V (BZX84C3V3) (was TH).
I let the meter run for a couple of days while thinking why the STD is such huge, and then I will adjust the 10V range against my ADR1001#1..
PS: could it be those resistors are such noisy?..