Star grounding is common in a studio environment...
True, but we're not talking about a studio. It's an "older house" (which means no RCD's either) with either suspect mains or suspect equipment, or hopefully and most probably it's just hum being induced on the mic cable. Even in a studio, it's really bad practice because to re-earth kit through other kit, because if you happen to connect two bits of kit on different phase power supplies (fortunately this is HUGELY unlikely, and you need to try quite hard to do it) star grounding won't help you if the one of the cases becomes live from a fault.
I do hate myself for being 'that guy' and having to say all this so I'm reeeeally sorry for coming across like that, but "then just touch various cases of your other gear..." is just not a solution. You say you don't care for the filter approach as it's not a solution, well at best re-earthing a PSU puts off the problem, it definitely doesn’t make anything any safer, and at worst it could be lethal.
I totally see that the required situation to arise for there to be an unknown fault in one or two bits of kit is unlikely, usually you would notice something before. But my point is that I just have difficulty seeing how re-routing the earth is a good solution, because however you look at it you’re not making it safer. Surely the safest thing is to find where the hum is being induced, and if it’s not being induced then to get the equipment checked? Which as I understand it is what kiddakota is asking how to do, which is why I suggested trying a completely different mains supply.
I don’t see why given the choice, taking any sort of risk with mains or even just a PSU is a good idea.
Once again, I apologize most profusely for seeming to have my 'safety hat' welded on to my head today.