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I think it would be a very special hand saw to manage not to shell the edge.
Some track saws have a special setting to score melamine before full plunge to cut it. That works very well but I still use a special blade which has rounded teeth in between more normal types.
When you think about how the 'set' of a saw scores and gouges it's not surprising the melamine shatters. I have had slightly better results with Japanese pull saws but the melamine coating is pretty rough on those.
Cheers, scoring sounds like a possible. The other issue I had was after the cut trying to take small amounts off to fit neatly, planing also seemed to tear up the melamine.