The shape of the top of the nut doesn't affect the way it plays, just the depth of the nut slots.

But you can file the nut down once the slots are the right depth to remove any excess height in the nut. Rub it with some fine sandpaper and you can then use some metal polish or rubbing compound to give it a nice polish.

A 1mm depth between the string and 1st fret is still quite high, and it could come down a bit more.