I don't run command and sound either; the electronics remind me of past work the mood has to be just right for me to enjoy them.
Interference is a case by case thing. I've worked on electronics that would refuse to operate correctly based on what outlet in a room was used, what type of hight voltage step down to local 440v was used, etc etc.. Just be confident very few folks don't track down their gremlin or have many (but a select few have put more than a fair share of effort to win... Cross the fingers; good luck )
The chicken wire is an issue, gypsum content of wall material is another. Either of the two can perform sheilding.
If I'm not mistaken the signal is run in the household ground. But regardless, one of the three is the carrier.
The answer is here somewhere if you search... but I usually try simple stuff by trial and error process of elimination and there's only two things to try and experiment with.
1. I'd start with the ground and try to simply run a wire along the "nice tunnel ceiling to household ground. (Assuming it has a modern ground installation). Use an outlet cover screw, that's should be ground. At the transformer is fine. If that didn't help, 2. a cheap extention cord would run the other two at once. But I'm pretty sure it's ground vs piggybacks on the two active lives.
How are you going to deal with the tunnel portals vs new track dia.? Tear it out, or only tear out what's needed.
It's always a shocker to me to a nice one like that get razed