That totally looks like the known issue in earlier cards with multimonitor.
So the card likes to down-clock to save power consumption. Usually the card is set to downclock pretty low, because that's fine with one monitor. But, in multimonitor, it needs the clocks to be a little bit higher. So it downclocks too low, and you see this issue.
Have you tried adjusting the idle clocks?
Also, I'm guessing the problem goes away completely with just one monitor?
As a test, can you run a 3D utility in a window, and move it to that monitor, and see if the issue goes away? The reason is there are 2 sets of clock values, one for 2D and one for 3D, and the 3D utility would trigger the card to use the 3D clock values, which are typically higher to make the problem go away.
The problems is exacerbated I think by your example video where you have a website that has a lot of embedded videos showing, where you need more juice to display them (in contrast to a plain 2D screen with just text and no embedded videos where the video engine is used).
My information is relevant to 5XXX series cards, but it may be a similar issue with yours, as it can be caused by a particular vendor setting their idle clocks too low. I resolved this issue by getting a replacement BIOS from the vendor, but the only difference was they bumped up the idle clocks. So it consumed a tiny bit more power, but worth it for the rock solid stability. You can edit your own bios if you want, then re-load it.
