Hi thomjohn,
With the action at the 12th set high (normal L5/32 H3/32 ) intonation will be hard to set if not impossible, since the string is stretched a bit when fretted. The pic's show a lot of relief and very high action across the board. The nut also looks worn. 1st fret low and strings sitting deep. Nut also looks wrong (sharp edge not good ! ) Nut to string contact should be about the same as the string width. With a sharp contact edge, string will cut into nut causing premature wear ( lowering 1st fret action ) and will bind and not tune well.
On the 6th string, press it between the 3rd and 2nd fret. There should be a very small clearance were the 1st fret is. (about .006 : thickness of 3 sheets of typing paper)
Here's how it should look :
Guitar Nut Removal / How to Replace an Acoustic Electric Guitar Nut:
I would say a new nut is needed and a pro setup done.
hippie: