Interestingly, I've discovered that when I put the same laptop I was talking about before into Suspend or Hibernation mode while having a paused video open in Totem, once I wake it up again the same problem that happens with the external LCD happens with the laptop's LCD.

It seems to gradually go out of sync. Sometimes takes it a few minutes to even become noticeable, but then it goes on to become completely unusable.

I'm starting to think this is a display driver issue, rather than some misconfiguration in the X server.