Arcade monitors almost always have adjustable geometry, so you can over or underscan them as much as you want. If the Lik-Sang box only works with progressive PS2 games (of where there are sadly very few), then it's nothing more than some wires and a sync separator (you can buy an LM/EL1881 for $cheap and build it yourself, in other words). You can get ncie sync off the composite video output in standard res, but not progressive mode. Getting RGB in progressive mode out of the PS2 is a bit harder since its sync on green is fubar'd (as in there appears to be no real sync at all, but there's often enough info for a monitor to reconstruct everything from the blanking pulses).
The way I did it was to chop the end of a SCART cable and use that. I would have used a SCART socket, but those are remarkably hard to buy in the USA. The quality is equal to that of a real arcade output (in fact, some arcades these days are nothing more than console hardware thrown in a box).