Hey Bluesman welcome to the community 
Sorry to hear this makes it unusable. You have a PS-2A which is the latest version of the Power Station and has improvements to the power supply in terms of filtering.
I can hear the hum when in Bypass (this is noise from your valve amp), and this increases when you go into Operate because you have the noise of your valve amp plus the noise of the PS-2A’s valve amp on top.
Sometimes this can be improved by detecting and changing a tube that is particularly noisy. The noise can occur due to random variation in the manufacturing process of tubes that increases the leakage current between the cathode and the heater element.
When cables carrying small, single-ended signals are close to PS-2A’s transformers, this can also be a cause of noise because the changing magnetic fields induce a noise voltage in the conductor.
But you sound like an experienced user, so I am sure you have tried different cables and moved them into different locations to see if the noise can be improved. A photo of the setup might help to see if I can catch anything, however unlikely. And if you do have a different ECC83 you could try swapping it in: How do I change the tubes and fuses in the Power Station
However, I get the feeling that these will probably not improve things too much. When you are playing the guitar, how is the hum? It is quite hard to gauge from the audio above the true levels. Are you based in the UK? I wonder if you are close to me; you could always pop over, and we could compare it against my PS-2A. PM if interested. I am about an hour from London.
Regards,
Dan