I'll respond to you first since you are the first user to mention the hum problem in this round. I'll respond to Ken separately tomorrow or the day after because I am not 100% sure you and Ken are having the same problem (and this is 3am in my timezone). From what I read, you heard the hum from the outboard Power Supply and it is 120Hz in your assessment, while Ken only mentioned noise from headphone output.
Your observation is correct, when you head 120Hz, it is likely a doubled of 60Hz after rectifier and that's why my immediate response was to check out the various frequently-mentioned sources of hum. For those who joined the thread only these few days, please check my test recommendation
HERE. For the record, switching power supply and power supply with non-digital dimmer features are the two biggest sources of ground hum. If you use a computer as your USB Audio source, the noise from the switching power supply will go into the DAC and then be passed to the amplifier via the USB Audio connection. Some USB has better isolation in their USB receiver circuit and stopped the pollution, others don't.
Yes, as mentioned in my previous post, we used HD800 and HD800S with HA-300MK2 and we didn't notice any excessive noise or hum in our test. We didn't use HD820. Since we have used HD800 and HD800S, we didn't perceive the need to test HD820 specifically, we just assume they are similar enough electrically.
You have mentioned that noise is volume independent, how about impedance setting? I assume you are using High impedance setting with HD8xx headphones, can you try Low and Mid impedance settings and tell us whether the noise level will lower when you switch the impedance setting to Low or Mid. If that's the case, the hum noise level is directly related to output power, so it is not a bug in the signal path, it can be an external noise that gets amplified LOUDER at high impedance because of higher rated output at this setting.
Will a better power conditioner/filter resolve the issue? It depends. In my experience, a filtering type power conditioner won't solve the hum problem you are dealing with. Isolation Transformer power conditioner might work (very likely), and Re-gen Power Conditioner will work in most cases, but you cannot connect your PC (with switching power supply) to the Power conditioner.
Erwinatm's comment is right on: bad transformer or electricity.
paradoxper provided the guideline to debug the sound system: by process of elimination.
If we can, through a series of tests, eliminated electricity as a source of your hum problem, then we'll arrive at the final hypothesis that the power supply transformer is having some problem. It can be a broken transformer shield that caused leaking of electromagnetic interference from the power transformer into the power supply circuit, just an example of different outcomes.