I think the good Doctor is on to something about the intonation. If this problem has been slowly developing over a long period of time, you should look down the length of the neck, from the head, and see if the body of the guitar has a pronounced bulge, or 'belly' between the sound hole and the strap peg. This is caused by the string tension pulling on the bridge and the top. The bridge slowly moves up, raising the action, and closer to the nut, slightly reducing the scale length, which screws up the intonation.

That's very hard to fix. I suspect the repair would involve replacing the top, and possibly 'pinning' the bridge to the soundpost.