Sorry you're having this trouble. Nothing mutes the joy of music making quite like a tech issue. I don't have any solutions, but bumping this in case more people will comment with ideas; it would suck for you to get this close to enjoying modular only to be stymied by annoying noise.
Though I don't have solutions, I do have a few thoughts.
* Is your audio coming through clean, but also has this noise, or is the audio itself distorted?
* Can you describe your external interface situation / what is the outboard mixer?
* What are you runnning your pre-amp module into / at what point are you introducing the balanced cables?
* Do you have a recording of the sound? Maybe one of the more keen-eared electrically minded folks here can identify it.
* Output module - I'm not familiar with your output module, and I certainly don't mean to bad-mouth a company I'm not familiar with, but perhaps it's introducing some noise? Also, it's description on the manufacturing page says that it's main use is to go from line level (significantly lower signal) to eurorack level (significantly higher signal). If you're already putting a eurorack level signal in there and adding gain, I'd imagine some noise or distortion would be introduced.
- Though I hate to suggest buying another thing, it might be worth trying a different output module, one that can attenuate the eurorack level signal, rather than add gain. What type depends on your workflow and what you're looking for. I'm familiar with the Expert Sleepers' ES-9 and Happy Nerding's Isolator, both of which I can recommend as being clean, but are very different. I've also heard excellent things about the cleanliness of the sound of Joranalogue's Transmit 2 and Frap Tools' CGM/mixer series. All of those directly interface with guitar / balanced cables and may make your system a little more streamlined.
Hope some of this is useful. Best of luck getting to the music making soon!