For the Ohms problem, it might make a difference of the "protect" capacitor at the input is connected. If this really is an MKT type cap, its DA might cause problems too with very high resistors. Just in case one could change it from MKT to MKP or NP0.
For the very high ohms ranges and thus very small test currents, the current source uses quite small voltages and might still have quite some meter internal leakage. So I won't expect really good accuracy above 1 M anyway. So those extra ranges for very hight resistance are not expected to be very accurate.
The INL data for the positive sign from szszjdb look so bad, that there still might be a well hidden defect. TiNs and Mickle's meters seems to be considerably better, though not really what one expects from a 8 digit meter. From looking at the schematics, I would be kind of afraid of INL do the self heating of R200 (input of the ADC), causing a U³ component. At least so far the data shown look good at least - likely really good quality R200, or maybe a hidden numerical correction.
It would be interesting to see how large the AZ mode current spike is. I thought a little about the switching sequence and from this the critical part could be with large negative voltage, especially the small range below -10 V. The step from switching between a negative voltage to a positive voltage should not be so bad: the guard from OP U107 should start low and may cause a slightly delayed turn on, but nothing bad would happen. However the other direction might be tricky. the guard level can be relatively positive and it takes the OP07 quite some time to come down. If this is slower than the LM399 and the 100 K resistors allow the gate voltage to rise, this could result in a gate voltage that gets too positive and cause gate current to flow. R83, C26 might be for this purpose, to slow down the switching. So they make some sense.
With a positive input the problematic input step would effect the GND reference in AZ mode, with a negative one it would be the input. There would be definitively a asymmetry between positive and negative voltages and thus possible contributions to input resistance, that might be nonlinear. I would definitely expect the input current to be voltage dependent.
The reported VDC drift problems might be due to the bug causing the input relay to get rather hot. So chances are it gets better when fixed.
The DCV transfer between ranges (e.g. 10 V to 1 V) is also a bit disappointing for a 8 digit meter. However if known the error might be corrected manually.
Another possible problem could be due to DA from the integration capacitor. This might cause some settling problems. So it might be worth doing a test like switching from a relatively high voltage (e.g. 10 V for maybe 1 minute) to 0 and record the data for the first maybe 1 minute at 10 PLC. One might be able to do this with changing from front to back. Without AZ there will likely be quite some effect, but who really cares about this. Depending on how AZ is done there might be some effect with AZ active too - and this could be a problem, especially if not known.
On trying to improve a little, it might be worth adding some caps in the feedback to U209 / U211 to produce the 17/-19 V references. This would add some filtering to the reference and thus reduce the noise of the ADC a little. Due to the modulation the ADC is sensitive to noise reference noise at around the modulation frequency (around 5 kHz). It is not very much, but avoidable.
The meter is still better than many 6 digit meters.