Verne-Bunsen

If you move FX Loop 4 from the parallel path up to either before the split or after the merge, does the problem resolve? The factor that your troubleshooting has not addressed is that only Loop 4 is set in parallel to another signal path. I suspect that if you move one of the other loops down there, then it would suddenly be the troublesome one. I have experienced "phasing" issues when running a pedal in an FX Loop on a parallel path, which I attribute to half of the signal being subject the small latency introduced by the extra cabling and the circuitry of the pedal itself while the other half of the signal is not.

Make sure that the "Trails" are turned off in the FX Loop parameters, as that feature will leave the return of the loop live even when the loop is bypassed. Any noise from the equipment in the loop would then be audible. I run an Earthquaker Devices Erupter (not a "quiet" pedal...) in one of my loops and it is completely silent when bypassed.

I've been thinking about it more and maybe that switch could be made to work? If it switches like I think (center common, switching between connection with the two outer lugs, which is just a guess without putting a meter on it...) then I think you could run two wires from the jack sleeve lug, one directly to one of the outer lugs and one with the 10k resistor inline to the other outer lug, then run the center lug to the jack tip lug. In this way the path from tip to sleeve would be a dead short in one switch position (through the direct wire) and 10k ohms in the other (through the resistor). If you have some alligator clips it would be pretty easy to give it a whirl, check it out either on a meter or just using EXP position indication on Helix.