So there you go. You have to have RCA to TRS cables with specific measures implemented at the TRS end at least for the console outputs -> tape machine inputs. Your existing cabling might work for the tape machine outputs to the console inputs, but you’ll have to experiment…
On that note, am I correct in understanding you hear the hum from the tape machine outputs when monitoring at the console, either when using headphones or control room monitor speakers? The RCA to TS cable with single conductor and shield is doing the same thing as stated in the reply from tech support for the inputs to the console…that is assuming the shield of the RCA plug goes to the shield of the TS plug, and then the “ring” and “shield” contacts in the TRS jack on the console are both connected, like tying the “cold” and “ground” together as per the instructions in the email response you got, because both those contacts touch the same “shield” section of the TS plug. So that should work…again, for the input side at the console. If you are still hearing hum at the console, temporarily disconnect the cables from the outputs of the console AND the inputs of the tape machine, so only the outputs from the tape machine are connected to the inputs at the console with your RCA -> TS cables. Hum gone? If it is still there then you’ll want to try lifting the shield from RCA plugs, so it floats at the tape machine end and only the signal pin is connected.
Audio signal is AC voltage…so the shield of the cable is not signal “ground”. That’s why I keep using the term “shield” because that’s what it is…it surrounds the signal conductor in the cable and shields the signal from RF and UHF interference in the environment, and then that interference, if induced into the shield, is shunted to chassis ground at the console end via the “shield” portion of the TS plug, and furthermore the “cold” side of the differential line input amp is also connected to ground, which essentially deactivates that side of the input amp since it is not needed…grounding keeps it from floating and potentially creating noise in the signal path. So you can lift the shield at the tape machine end if you need to and maybe that will resolve the hum if necessary. This is not at all uncommon practice. Your problem might be if your cabling has molded strain relief and jacketing at the plugs, you won’t be able to access connections and implement the modifications. In that case you’ll need to buy aftermarket RCA plugs that you can solder on in place of the factory molded plugs on your cables if that be the case, and only connect the signal conductor…leave the shield disconnected.
On the output side you can still use the single-conductor shielded cable you have, but you’ll have to buy replacement TRS plugs to solder in place of the existing TS plugs, connect the signal conductor to the tip, and the shield to the shield, and leave the ring not connected as per the instructions from the tech support email you got. And here again if hum still exists you may need to implement the same lifting of the shield at the RCA jack as I described with the tape out to console input cabling.