I just took delivery of a ZDac to replace a MuFi VDacII. The ZDac is dead quiet, but I might also be "cheating."
I'm running Balanced AQ interconnects, and have the ZDac plugged into a Transparent PIMM (that's also providing the power to my CDP). The power line itself is running audio only; no dimmers; no computers; and no video monitors.
Have you tried running the ZDac isolated? That is, by itself, away from other equipment, and without anything hooked-up to it. If not, consider plugging it into a quality surge protector/conditioner and, in turn, power that through an outlet that's on a line that isn't being shared by anything.
If the ZDac still hums after you've "quarantined" it on a clean line and by itself, then it's likely the unit is the source for the hum. If you do get a hum, try repeating the quarantine on a clean line at a friend's house. If the repeat trial also generates a hum, then you know it's very likely the unit itself.