Just to add more context, I traced the circuit from the V input of the meter up to the "ADC" IC.
By the way, quick insight, this "ADC" IC is usually lasered off in these series of Metrahit DMMs.
However, this one was left intact and I could determine what IC it is: it's a Fortune Semiconductor FS9704B.
This looks to be a full blown multimeter IC but, in this case, Gossen seem to have decided to add a TI MSP430F149 as the brains of the multimeter, which then talks to the FS9704B via bus transceiver ICs.
Coming back to the topic of this thread, as I was saying, I traced the circuit from the V input up to the FS9704B IC (going to pin 18) and it all checks out.
I also traced the circuit from COM to the same IC on pin 25 and there are not issues there either.
So, there is no issue with the input analog circuitry, as far as I can determine.