Thanks for the suggestion. It's clear to me that AD8675 isn't suited for input voltage outside the supply rails. Unfortunately AD8675 shows already phase reversal with input voltage within the supply…
For low impedance circuits, voltage noise is more important than current noise.
For high impedance, the reverse is true.
With 2.8 nV/rt-Hz, this is definitely an op amp that is designed for low impedance circuits,
so I would have never chosen to use it in a high impedance circuit.