Hi!
I have a Steinberger GR4 which has the same zero-fret and “string mounting system” at the nut. It has significant groves on the zero-fret and only double ball ended strings without any adapter have been used. When I am bending certain strings on the frets closer to the nut, they will temporarily pop out of the groves, which feels strange, and you hear a faint “ping” sound - but this is on the “other side” of the string and will not be picked up by the pickups. It doesn’t really bother me and this guitar is over 30 years old, so I guess the groves will “stabilize” at some point and not deteriorate any more.
This is a common problem of the zero-fret: I also have a Vigier Guitar which has a stainless-steel (!) zero-fret and still quickly developed said groves. As this is a known issue, Vigier split the zero-fret into six little frets, so that each string has its own zero-fret. This allows you to change only the specific zero-fret, which has a grove and which bothers you.
Michal