It's all in the drivers...
After months of frustration, I think it's time to share the results with the world.
I've changed my Gigabyte motherboard (free upgrade to a version with fixed chipset). I've RMAd the graphics card and replaced Gainward with MSI, still GTX 570. That was all no go. Problems persisted through hardware changes.
Finally I've discovered that kernel upgrade from 2.6.35.x to 2.6.38.x decreased the frequency of issues.
Then I've disabled all kinds of acceleration for Flash. This basically fixed stability, but artifacts were still appearing every week or so.
Then driver 275.09 came out...
On the new driver, everything works as intended, fast and stable for weeks without reboot, until Flash touches the GPU. It was all a driver problem and the driver still isn't fully fixed (since Flash, a normal usermode application can sometimes freeze or crash the X server). But for now it's enough, at least I can play Quake finally ;)