As I mentioned in the OP, when the monitor is malfunctioning, I have
swapped the DVI cables between the monitors. When doing so, the
malfunctioning monitor continues to malfunction while the other
monitor (the one which has never malfunctioned) continues to function
properly. So from this, I believe the computer & video card are
functioning properly. Am I making a valid assessment here?

Yes, of course -- that's Troubleshooting 101.

What's going on is that the video information is being lost, and the pixel
"twist" is being forced all the way one way, then all the way the other way.
As to the cause...