Try setting the witness points if you haven’t already. That can fix a lot of tuning and intonation weirdness. Like Beej said, check the nut slot also. It should have an angle down towards the tuning key with the fretboard edge being the highest point.
Setting witness points on strings often comes up as a suggestion to fix poor intonation, inability to set intonation due to lack of saddle travel, excessive string height and mysterious buzzes at the bridge or topnut. Witness points should be set on all strings on any stringed instrument. The principles and the problems caused are the same. The strings were changed on a BEAD 4 string with string through body and pictures taken before and after the witness points were set. The pics were converted to gray scale to make the text easier to read and filters used to enhance the strings.
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