"Dirty" power in your building then. Not sure what exactly that is. Everything not balanced in some way? The house ground (third prong) may not even be attached. I've seen that b4. It can be dangerous in certain scenarios. Seriously though, the hum wouldn't come from the digital circuitry. I don't know why you keep assuming that (unless you're having me on). The fact that your devices are digital is just a coincidence. At worst, it could be a chip picking up EMI, but whether the chip operates as an analog or digital device is irrelevant. Still, it's highly unlikely. The chips are surrounded by shielding. In any case, since it only happens when your strings are open, I think it just has something to do with the way those devices are powered/grounded. I would be particularly wary of using the ground lift option on any DI devices in your building. It can be dangerous anywhere.

I wonder if attaching a wire directly from the case of your HD500 to one of the wall outlet ground prongs would solve it? Only if that ground prong is actually grounded, I'd guess. Do you get the hum if you disconnect all the the HD500 outputs and just use headphones with it? If not, it would indicate some kind of interaction with the gear you monitor through.