Faraday cage should cover that no? Styro even mentions in the linked video that he needed to encapsulate his workshop in one in order to not get angry visits from the FCC. I'm sure for something scaled up like this you might want to nest a couple of them together.

Again, not an engineer, I could be (and likely am) wildly off base here. Not sure what makes it such a terrible idea though. I am pretty certain that a MW-scale Tesla coil probably wouldn't blow out a larger area of communications than, say, nuclear testing would, and we do that all the time in the Midwest.