You’re right, don’t discount N-E faults, they can happen all over the place. Check your cooker, immersion heater, toaster. At my parents house years ago, the electrician fitted a new consumer unit and discovered a latent N-E fault in a ceiling rose, been there for decades probably, really hard to find.
I think your original idea of using your isolation transformer is a useful avenue for ‘individual appliance’ test. It will stop your house RCD from tripping while you are trying to measure. You’ll need to ensure/know that the secondary winding is earthed and connected to the DUT CPC to recreate the protective conductor return path, and to keep your equipment enclosures safe. Take all the measurements you want on that local system. Note that unless your transformer is one of the medical grade ones that has an interwinding screen, there will be a small but not negligible amount of leakage current through the transformer.