Mark,
my recommendation is to connect the chassis of the OPPO with one or more chassis of the other components. This will ensure that you are in no danger from an electrical shock. It should also be easy to try and test the effect. As I said before: this serves as the "easy" route for the current to flow from one ground level to the other. Please take a look at the links that I posted before, because I couldn't explain it any better and the topic is extensively covered.
People seem to think grounding the chassis together solves the problem (it might reduce it some). Where that basically is the problem. The chassis are already grounded to each other through the audio cables. And that is why optical sometimes fixes it because you BREAK the ground.
The easiest thing to do, is do what Oppo intended which is not ground it.
I believe Gary added a grounded cord and socket with the new power supply, thinking more is always better.
I must have a dozen IEC power cords sitting draws. It's a requirement to being an audio nut. You must too. Just take one and snip the ground pin off. The original power cable as VK verified had no ground !!!
Basically you want a single point to earth ground for the entire system. The Oppo and probably the amp. Amps have a lot of current and high voltage so they are often grounded. DVD's/CD are light duty so they usually double insulate just the power supply and not ground the chassis and let the ground (Audio Ground come from the amp through the audio cables).
Think of it as like a tree spanning out from the trunk. Right now you have two paths earth (two tree trunks and one tree). And they are fighting over which which way to sway in the wind. The suggestion by NutFlush is basically saying lets make the branches between the two trees bigger so they are forced to sway in the same direction. The other solution is to pull up one trunk and let it freely sway in the wind again.