I would raise the two tremolo posts up by a few mm.
Also, make sure that the neck has a slight concave bow in it (like the top picture), and not a convex one (bottom picture).
But you are also not going to get a true picture of how the guitar is set up until you fit all the strings and get the correct tension on the neck. That will add more of a concave curve to the neck and help raise the strings away from the frets.
You should now be at the stage where you can screw the neck on properly rather than clamp it.