Hey Age of Geburah, your explanation was excellent
, I just wanted to clarify.
So yeah, the string travel down to the fret is pulling it sharp, probably more noticably the nearer to the nut you play...ie the 1st fret is the sharpest. So string travel down to the fret is minimized with proper nut height, truss rod adjustment for very little neck relief (straight as you can get it...), a good fret dressing if required (not usually), so I'm describing a good low action set up. Of course avoid buzzing etc. Also thicker strings resist bending
while being fretted, so they help. They sound fricken great too
Okay, here's where I'll try to help with something you haven't already done...at least I hope I help...
Try this...instead of the standard method of intonation (where the 12th fret harmonic is compared to the 12th fret fretted note...)...tune your B string by fretting the second fret, making sure that note (C#) is as 'in tune' as you can get it. It'll be sharp btw. Unfortunately the tuning can 'wiggle' due to finger pressure...do your best... Now check the C# at the 14th fret...move the saddle as necessary (presumably away from the neck, lengthening the 'speaking length' of the string), retune to the second fret note, compare to the 14th fret again...
It takes no more time than the standard procedure, and may yield the desired results...a guitar that at least plays in tune with
itself
Or
(wowlongfuckingpostsorry)
You may wish to do this comparing the first fret C to the 13th fret C instead...these will play even sharper, or 3rd fret to 15th...your call.