I was actually thinking of playing with the idea of putting a core around the speaker leads to see if it made any difference when I read your post. Needless to say I tried it and it had no effect on the noise. But... while it was running I unplugged the power from the hardrive and the noise went away. So I looked at the power supply and noticed the fan wasn't running. I had a new spare here so I swapped it out. Works fine, but noise still there. I may check the caps on the motherboard itself next. You may be right on the +12v feedback of sorts from somewhere.
The monitor started flaking out again, which made for a good time to dig into all this again.
This time I had another monitor ready to hook up to it and see what was going on. At first it seemed to be a motherboard issue because when the original monitor went blank I hooked the other up and it too was blank. But come to find out it was just due to a random lockup up the system. Next time it went blank I hooked the other up and the other montior came up fine. So I then looked closer at the original monitor and noticed it had no heater glow at all, no raster when turning the screen voltage up, etc. Not just a horizontal failure. So it was like it was firing up and then immediately shutting down. Later on it came up and worked great for several hours.
Still gonna plan on capping it completely once I get a list together as I haven't seen any "kits" for it yet. Will probably cap the motherboard as well.
Then I also came across a bulletin on the ArcArc site that I may check into and try. (see attached) Which could possibly be what it's doing according to the symptoms.
Ever seen that additional cap put on any of these monitors? (worth a shot)
EDIT: Just fired it up again this morning and it's working fine again.

Where's the "pulling your hair out" icon when ya need it.