Voltage and Ohms often share some of the same resistors in their divider networks. But they don't usually share divider resistors with the current sensing. All 3 might also share some of the same connecting switches, either electronic switches, or mechanical.
I've only worked on a few DMM's, but yeah I wonder what's wrong with the current measurement, and if it's related to the others ? Usually, the amp signal into the DMM, takes a different path right away, than a voltage signal. But then their sampled signal, might go through the same analog switch IC's.
If only the ADC section had a problem, I'd expect errors on AC too.
I'd trace the path of the V/R into the DMM, and check their divider networks and switches, and then see where Amp signals go.
Here's a link to some manuals, but I don't see a service manual, maybe it's too new a DMM by the late 90's ?
https://www.manualslib.com/products/Fluke-8846a-2791364.html