Before we start: It is worthwhile to note that all strings must start rom the same height at the peg heads. I had an intonation problem lately and it turned out my B string wasn't starting at the same height as other strings at the peg head.
Given how the string goes Sharp at few places and Flat at other, this case is very different from a Gauge-Change, Saddle problem or a Truss-Adjustment.
A string's pitch / note being played basically (there are other factors but these are most significant ones) depends on its Length from the fret held and the bridge (called effective length), tension in string and Density of String (Mass of string per Length, not volume). Leave out Tension & Density because they are string specific and you've tried different strings as you say in the question.
Now Length. Normally Intonation goes gradually sharper or gradually flatter. This fact will be obvious if you realize that either the Starting Length (Open note) is more or less than what the Guitar is designed for or the string is at an angle to the fret board different from what it is designed for therefore each fret corresponds to different points on the string than what the guitar is designed for.
Knowing the inner workings, you guitar is going flat at some points and otherwise at others means that this case is not usual, not the Starting Length (Saddle Case), Not the Angle (Truss Rod case). It is most probably the neck itself maybe affected by weather, changed its profile.
Answering your question. Nothing can be said for sure. Best bet would be to Take it to a Luthier, like Tim says in the comments, and it might happen that the luthier will suggest reprofiling the neck. Reprofiling is, Maybe a little given the COVID-19 situations but otherwise, not like very rare and very worrisome a job,. A lot of users here at StackExchange have gotten their guities' necks reprofiled too.