I'm sure the cables have not got to Norway yet. They likely will arrive sometime around the middle of next month between February 8 and 15th.
So the cables arrived today. I have not had the time to do a lot of testing, but initial testing does not seem to give the desired results. My small tests have been as followed:
1) I first tried to just swap the old RCA-XLR cables with the ones TSL Guy had produced, leaving everything wired as before outside of this change (so between the two units that means there are 3 x RCA-XLR cables, 1 x minijack for trigger and a speaker wire running between the chassis of the two units). This seems to produce the same outcome as the old RCA-RCA cables had (the ground loop, however potentially a little more subtle, though it is a long time since I had the RCA-RCA cables connected so can't fully remember the exact sound profile and sound level the ground loop was producing). The "popping"/"clicking" noise that the old RCA-XLR cables were producing is however gone. Further, it is acting very similar to the RCA-RCA situation in the way that at times the ground loop seems to suddenly go away (almost dead quiet), and then it just reintroduces itself. I have no idea how this is happening, but assume it has something to do with the speaker wire running between the two chassis.
2) I then tried to remove both the speaker wire going between the two chassis, as well as the trigger cable, but this just made the ground loop even more noticeable (meaning the sound level of the ground loop is higher).
3) I also tried connecting the speaker wire between the two chassis, leaving the trigger cable unconnected, but this seemed to give the same effect as 1).
This is so far a sad outcome, but at least it was worth the shot, and I would like to thank TLS Guy for producing the cables and shipping them my way.
Obviously, if you have any recommendations for what I should be trying before reverting to the old RCA-XLR cables please let me know.