With the original zener back in place the meter is stable and within a couple ppm of your other multimeters? You believe there is some significant issue with AD reference voltage?
Besides a self-test that is not officially documented, is there any evidence the meter is not performing correctly?
Are you suggesting that a $6,130 7.5-Digit professional level bench meter being marketed as "high stability" is acceptable to perform with 55% worse stability than a Siglent 6.5-digit meter that costs over $5000 less?
Are you also suggesting that those "undocumented" tests that accurately describe the issues the meter has, are not evidence in and of themselves?

Like many Keithley meters the 2010 has issues with low frequency noise. This is unfortunate, especially as there should be a relatively simple (for those who have the source code) fix in the firmware to get quite some improvement. This effects just such stability measurements or DC measurements with a time scale of some 10 seconds to 1 hour or so. With there unfortunate way of averaging the AZ data they can get a small (like 10%) improvement on the short time (like < 0.5 s) noise, but it could be a huge penalty (like 5-10x) the noise at longer avearging times (like 10s - 10 min). With a simpler AZ mode without fancy averaging the Allan deviation curve should continuing down like square root time until thermal fluctuations from the input take over at maybe some 5-30 minutes. I don't have much hope they would fix it for the 2010, but maybe for the DMM7510 and DMM6510.
So yes for some time scales the K2010 could be less stable / more noisy than something like SDM3065 or HP34401, maybe even a Hantek 3065.
A strength for the K2010 could be with the 100 mV range and current measurements - it still depends on how much 1/f noise from the amplifier come through.
Another point can be the long term ( days and months) stability - here the measurement of the ADC gain in the background can help and can allow the relatively good accuracy specs (24+4 ppm) for the 10 V range. It is doing some kind of ACAL for the 10 V range in the background. With a well aged LM399 the meter long term stability could be even quite a bit better.
The current pricing is more for a legacy product some still to replace an old one. At this price it is hardly competitive for new users. There are now better performing meter like the DMM7510 and KS34470 available.
Having the current setting resistor external for the tests could be a good idea. A pot and maybe the decade would want some 1 or 2 K series resistor from protection against accidently too low a setting.