If it only happens at the third fret or higher I don't see how anything happening at the nut or especially behind the nut could be at fault.
Just out of curiosity, are you muting the other strings? Sometimes I'll get harmonics on certain notes and it's from other strings vibrating that I'm not even playing.
Just out of curiosity, are you muting the other strings? Sometimes I'll get harmonics on certain notes and it's from other strings vibrating that I'm not even playing.