There's no reason you have to connect the secondary to earth at all. This is how a lot of medical equiment (under IEC 60601) and test equipment (under IEC 61010

There's no reason you have to connect the secondary to earth at all. This is how a lot of medical equiment (under IEC 60601) and test equipment (under IEC 61010) is designed. If earthing it makes everything worse, just don't do it. The NEC might or might not have something silly to say about that, but when you have a giant custom-built Faraday cage, I think most people will be understanding that you might choose to call it "equipment" (and thus, for example, claim that 61010 applies) rather than "building wiring" (so not NFPA 70). You can also earth things in some really weird ways. My favorite was to connect the secondary to earth through a 12V bidirectional TVS diode. Apparently this stops a lot of nuisance issues while still allowing serious currents to flow. Unfortunately, you want a bigass TVS to do this, and those are rather capacitive. So you still end up with RF issues. (No, you cannot use this to make an arc fault detector. Or at least, I couldn't do it.) Electrostatically shielded transformers are not really stock items. You will usually have to get them custom-built and they will usually end up as expensive, higher-performing C-type cores. Shoutout to Triad Magnetics for being very nice to work with as a custom magnetics vendor on that horrid project even though the project was cursed and we ended up going with someone else (which we should have known a lot earlier and not strung you guys along, but engineering and management had different aims there...), right up until it got cancelled.