I think I know the type, if it were me I'd be very wary of using anything abrasive, I assume the scratches are on top and visible as soon as you walk in ( that's what we thought).
Is there anywhere where you could experiment, an edge or underneath maybe to see what the various polishes can do?.
Alternatively you might obtain a similar off cut from some where to practice on.
It is quite likely there is some good advise on the web, google 'gloss laminate worktop repair' or similar.
Good luck