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The most universal sample rate for the PS2 is the standard DTV 858 samples/line for 60 Hz and 864 samples/line for 50 Hz.
An H.samplerate of 686.4 for 60 Hz (or 691.2 for 50 Hz) is theoretically optimal for games that have a horizontal resolution of 512 pixels, which includes a lot of PS2 games but not all. However, the display is likely to treat the resulting output as having square pixels, stretching the picture by 25%.
If the monitor accepts the picture when in Line4x mode, you’re likely to get the best results with that, with H.samplerate set to 858 and the Allow upsample2x mode enabled. Note that the picture is probably still going be a little wider than in Line2x mode (10% or so).
Edit: The default H. synclen is 62 and the default H. backporch is 57, in 480i mode.