Nut or Zero Fret?

This has probably been discussed before, but I am too lazy to go back thru the archives. I've build dulcimers both ways; zero fret (my McSpadden kit came this way) as well as with nuts made of mycarta, ebony, bone, and ash. Pros vs cons of one or the other?

The zero fret on my McSpadden has gotten "groovy" and if I dress it, I'm going to get buzz on #1. I've got a CBD that I made for my grand-daughter that has the same problem. Right now I have a tiny piece of plastic under the string with the groove, but it keeps popping out. I really don't want to yank the frets out to replace them, but I guess I'm going to have to. I do not think that I have enough room to cut a slot to put in a nut in place of the fret, because there is a "pseudo nut" behind it to hold the strings in place (see photos).

Thoughts or suggestions?