The nature of tube amps is they are an old technology and create noise, even when idling. Some are better than others.
One thing I have found is an isolation transformer really cleans up a valve amp and the HD500 and the guitar.
First though is your guitar. Some pickups are really noisy single coils especially and even some humbuckers can go microphonic easily.
Next is on the HD500 both inputs are active. The Aux is quieter when on the input page deselecting "same" and choose "variax".
This makes a difference.
The nature of the HD 500 high gain AMps and FX are noisy as they are modelling the real thing which are noisy.
Noise gating can help but work on the above first.
The isolation transformer really helps the hum and I'd recommend one.
Correction: Actually I reread your post it is the hiss from the amp you wanna kill.
There will be some hiss regardless from the amp as it is the last link in the chain apart from the speaker.
Hum gets on the power and the HD or any amp will magnify it. But make sure your guitar is earthed properly and even shielding can help it be not so sensitive. The pickups pickup stray interference easily and you might have to hold it just so in the one position that is quietest.