I started looking at this issue again. A poster asked if the issue occurs if the PowerColor Voodoo2 is moved to other systems; yes it does.
I swapped the bus switch PI5C3384Q for that of the S3L38Q found on my dead Diamond card, as well as FB6, C36, and C38. The problem still occurs, but I am noticing that it is more transient now. If I let the system stay on for a few minutes, the on-screen noise tends to go away. It seems like the noise was a bit more consistent when I tested it out 2 years ago, but hard to say due to the passing of time. I decided to keep S3L38Q, FB6, and C36 from the Diamond card, but put backC38 for aesthetic reasons. Symptoms same as noted in last sentence.
I didn't notice any transient noise with the other 2 or 3 brands of Voodoo2 cards I tested. I don't think it is any coincidence that both of these PowerColor Voodoo2's exhibit the same behaviour. Could the PCB design alone account for this, e.g. poorer ground plane design? The only item I didn't remove was the VGA connectors. Possible? But seems highly unlikely. The VGA connectors on my other cards also don't have a shield over the back of the pins.
Another thought I had was related to the 1084 voltage regulator. My other Voodoo2 cards don't use a 1084. Perhaps this regulator creates more noise than the others? It is positioned right next to the bus switch. I noticed that the Gainward Voodoo2, which also employs the 1084, has the 1084 positioned way far away from the bus switch - on the other end of the card.
Plan your life wisely, you'll be dead before you know it.