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The built-in flash waits until the shutter is fully exposed, and then fires the "go" signal. Even when the built-in is set to "--", there's a contribution. It's very low, but it will still be visible as catchlights in eyes, and reflections off of glass. Sidelighting of wine bottles, for example, is impossible.
I've seen some testing of the IR panel in this regard, and it doesn't get rid of the light completely. The SU-800 is perfect...except for its price tag.
Another solution that is free to try is to use the flash in Auto FP mode. Set custom setting e1:Flash Sync Speed to "1/250s (Auto FP)" and then set your shutter speed to 1/320s. The SB-600 will now fire in Auto FP mode. This suppresses the built-in flash completely. The reason this works is because the "go" signal is given before the shutter opens. You get a reduction in flash power, but it may be enough...depending on the lighting setup.