Could you tell us your method?
Sorry, I don't understand this. By definition, the 12th fret harmonic is the octave of the open string. How does a harmonic "begin sharp"?
The string can't "stop too close" to the fretboard if the nut is in the correct position, and if the frets are in the correct position. As I said above, if the nut is cut incorrectly so the string leaves the nut somewhere further back than the fretboard edge of the nut, it will affect the intonation of the guitar; the frets will be relatively "in the wrong place". This is why:
Imagine we have a guitar with a moveable nut and moveable frets. Lets say we start out with a scale length of 30". The 12th fret is half way along at 15". If we move the nut 1" towards the headstock to give a scale length of 31", then the 12th fret will need to be moved the same direction by 1/2", to 15 1/2". If we move the nut but don't move the 12th fret and leave it at 15" from the bridge, the string fretted at the 12th fret will be 1/2" short, and sounding sharp relative to the octave and the octave harmonic.
This is why mfowler should check his nut, as this is his symptom, the fretted 12th note sounding sharp relative to the open string and the mid-string harmonic.
Could you explain this further? The centre of the string being the 12th fret, a place we can fret, or am I missing something? Thanks.