I have fixed this by shimming the nut slot (on tuner side of the nut) with wooden veneer. My veneers run .6-.8mm so they generally need to be thinned down to fit for this application. The veneer can be sanded or scraped to achieve the right thickness.

I keep a range of different wood veneers on hand to try and get the colour to match as closely as possible to what I'm shimming, but because it's made of real timber, it can be stained to match as well.