... exactly. The schematics looks nice, but what they do is rip open the bridging relay before the connection to the multimeter current input (including the shunt) is established.
To me it looks like a beginners fault when programming the relay timing. Unfortunately, they refuse to work on this bug.
I've got the same combination running here and since I'm rewiring a setup currently, I used the opportunity to do some testing to try to replicate your findings. My firmware versions of the relevant components are:
M300 (Mainframe) - 00.02.00.08.00
MC3065 (DMM) - 06.01.01.25
MC3324 (MPX) - 00.01.01.03
Setup: Initially I routed the current to be measured (70V PSU connected to a 68k resistor ...because it was just lying around on my desk...) connected to a single current channel (first and second screenshot), and connected in series to all four current channels (third screenshot). I initially configured the acquisition system to scan alternatingly the current channel and a voltage channel (either on the same module or on a different one, this wouldn't make any difference). For the second configuration, I scanned the four current channels in sequence, then a digital port (that isn't related to the DMM module at all) and finally a voltage channel. This scheme relates to the third screenshot.
Findings: With only the first current channel connected, I didn't find any problems or interruptions of the current flow, whatsoever. Some ringing could be observed (probably when the DMM is disconnected and reconnected from/to the current measurement multiplexer) and the voltage drop across the shunt (100mOhm @ 2mA range) is present during the current measurement. The modified setup revealed more interesting details: While switching between the current channels, everything's fine again (some ringing present but it decays in a few hundred nanoseconds, and some picked-up noise due to the unshielded wires). But after current channel 4 had been read and the instrument reconfigures to voltage measurement, I get a clamped glitch (with some contact bounce) of 400µs.
My interpretation is the following: The multiplexer card is working correctly but the input configuration relay on the DMM changes state too quickly. There should be introduced a small pause before the DMM is reconfigured after measuring currents. Unfortunately, at least from the panel of the instrument itself, it's not possible to insert a "slot" with a "pause" in the acquisition list that just disconnects the current inputs (and hence shorts them) so only in the next step, the input of the DMM will be reconfigured. If this is possible via the "UltraAcquire" software, I didn't check. One possible and simple solution in case not all current measurement channels are in use would be to "dummy"scan an unused channel before changing over to voltage measurement mode. I also found that the current measurement channels appear to be clamped via two silicon junctions in series (shorted bridge rectifier?) so the voltage drop, even if the switching sequence is troublesome/faulty, should never exceed 1.4 volts. If this is a problem for the external circuitry depends on the particular configuration. Evaluating 4~20mA sensors should be okay.
Cheers -