I sounds to me as if you have a volume control switch malfunctioning.  You could very well have a tube that has gone wonky though.  You do have a switch on each stereo chanel so troubleshooting is much easier. Take pencil and tap gently on tubes with the eraser while unit is on.  Tap on the volume control knob also, trying to duplicate the static.
1) check each side for problem one at a time
2) if one side does it and another not try switching one tube at a time and checking
power on and off in between of course

Thanks Walt, the volume static seems to diminish after an hour or so of warm up. I tried the troubleshooting technique you suggested and it seemed like the right side showed the problem but the volume knob started to behave before I could swap any tubes. I'll get back on this!

Walt, the ZP3 was initially on a shelf right above the amp. Yes, using shielded cables at first - nothing special, auvios.
I moved the system out of the rack to another location, amp and ZP3 now side by side. Connected to my old JBL control monitors which are less sensitive. The hum was there but noticeably reduced. Then, oddly, I reconnected to the other speakers and the noise from the phono stage all but disappeared. I now have (not hugely objectionable) hum coming from the arm at higher levels but the phono stage and amp are quiet. Now happy with the sound. There may have been some interconnect problem combined with a bad location for the components. Initially, I was using the auvio shielded cables but while swapping things around, I substituted cheap unshielded cables. I'm thinking now that I need to find the best location for the components and keep fooling with the interconnects. The cheap unshielded cables seem better in some but not all cases compared with the auvios (which I know aren't all that hot either!)
Steve said a tube was causing that static sound from the gain control. but I'm not going to worry about that for now. I'll get to the tubes later. I will however swap the rectifiers as you suggested and see how that affects things - Thanks!