Hennng, by TUNING at the 3rd and 4th frets you've just added an extra step of complexity and reversed the whole deal.
TUNE the open strings. Then fret notes up the neck and record if they are going sharp or flat over the first few frets. If the notes are going sharp up the neck then the point where the strings exit the nut slot needs to be closer to the 12th fret. If the fretted notes are going flat as you fret up the neck then you file the contact point away from the 12th fret and towards the head.
OK, Now let me reverse it all. Lets say that the instrument is well intonated on all frets from the first fret up if you tune it so that the first fret is in tune and then just the open strings are out of tune.
If the OPEN strings are sharp, then NOMINALLY, we would say that the intonation is GOING FLAT and this is because the nut is too close to the 12th fret so you would file it back towards the head. If the OPEN strings are going flat compared to the fretted notes then nominally the intonation is going SHARP and you would move the nut contact towards the 12th fret by filing the end of the fretboard back or placing a shim on the fretboard.
TO be honest you need to be careful about reverse thinking until you have your head around it although I can see that it could be useful to reverse think it.
Stick with tuning the open strings first and then assessing if its going sharp or flat.
Also and importantly. Measure! And then measure again.
If the intonation is going sharp then measure where the nut is placed in reference to the 12th fret. If the intonation is going flat then where is the nut placed. If the intonation is spot on then where is the nut placed compared to the 12th fret.
The first step. Is the Nut placed PRECISELY where it should be?
If it is then good and what is the intonation like over the first few frets.
If its not precisely in the right place then adjust it but first measure what the intonation is doing.
The aim here is for you to know whats going on and place the nut exactly where you know it will need to be.