When i'm trying to play octave chords on the frets with the best sounding natural harmonics (5,7,12) ,the harmonic is caught in the chord and it feels out of place.
Anyone know a way to get rid of this ? Guitar modification,exercises,etc... ?
I think the best thing to do would be working on how your actually holding the "Octave shape." If your fingers are bent the right way from improper technique, it'll grab the harmonics and clash with what you're playing.

Try arching your fingers a bit more when your playing and see if that works.
Skip the username, call me Billy
You have to make sure you're muting the open string. Simple as that.