OK, so there's still something that's different in the way the program is talking to your monitor. Using Desktop resolution should not produce a click if the following are true:
1. Bits-per-pixel are also the same. You've said that they are all set to 16-bit, so that's not it.
2. Refresh override is not set in DXDIAG. If it is, then the monitor will click when it switches from the Desktop to any Direct3D application. Even so, I don't see how this would greatly affect the frame rate, and it should work the same for both versions anyway.
One more minor thing to test: Could you switch the French Angels with some other fish? The French Angel now uses mipmapping. Any fish without stripes should be safe.
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