Hi Solafide.

with the nut, take a fine bladed saw, like a junior hacksaw, and cut a line across the width of the plastic nut more or less in the Centre. Take that cut down through the nut until you are almost at the base of it, but don’t break through.
get a scalpel or a razor blade and run this around the edges of the nut, jus to break any glue spots.
You then take a pair of flat nosed pliers, and use these to crush the plastic nut sides into the cut you’ve made, this should pul the sides and the base free of the fret board without damaging it.
knocking them or levering them out tends to cause pull out and can chip the board edges very badly.

if you have the ability to plug and re drill the neck screw holes, I would do so. It will piss you off no end to create a beautifully finished guitar only to have a crooked neck plate!