There should be very little difference between the TQ2 and EA2 relays - mainly a different manufacturer.
The high voltage MOSFETs, if they fail, they usually fail short and one can check this in circuit if needed.
At least the K2000 the ACV and ACA singals are both from the RMS converter chip output. The ACA signal has an additional low pass filter and would thus be the path for slower readings. Both paths should be possible for voltage and current - it is more a question of the reading rate.
Overall the K2010 looks very similar to the K2000 in the front end. The main concept is as follows:
Relays and JFET switching (Q104,Q105,Q18,Q109,Q113) are used at the very input to choose between the voltage input, the high side and the high voltage divider.
Than come a zero drift buffer. In the K2000 this is an LTC1050 (may be a different type in newer meters) with a bootstrapped suppy.
In the K2010 there is an additional pair of JFETs to support the AZ OP-amp for the higher frequency part. This is to get lower noise and maybe allow for a bit more filtering.
The multiplexer chip U163 (+1/4 of U176 or U129 for the K2000) is than choosing which signal gets to the main amplifier stage with gain. Signals here include the buffer, low side sense, the current shunts, the RMS converter output, ground and reference levels to check the gain.
In the K2000 the amplifier is with 2 OP-amps, with the K2010 the main amplifier is with the discrete JFETs, the LM394 and more parts.
The auto zero loop would normally keep the JFET part fixed and switch U163 for the signals (input, ground and reference voltage - depending on the speed).
The idea of checking if R319 does to 1 V was the analogy with the K2000. As the K2010 has 2 references, it could be that this would be the 6.4 V reference, though I don't see much need for this (mainly a self test thing).
So far it looks the issue with the meter in question here seems to be the JFET switching part seems to be open. This than cause the hum for the signal from the AZ buffer. My prime suspect would be the comparator (LM339) that controls Q104 to be struck at low and thus never connecting the input.