Hi Marianne,
Thank you, thank you, thank you!
You're suggestion of getting out of Live View and moving the focal point off-center and re-centering for solving the "Auto AF fine tune is not available at current focus settings" problem worked for me after much frustration.
Also, your later comment that one should not re-focus in the middle of collecting a set of AF fine-tune values. This solved my problem of getting a wide spread of values with which I could have no faith.
I do have a question. Today was my first attempt at fine tuning. Following all your suggestions, I started with my Nikon 200-500mm at 500mm fl on my D850. I first collected 8 values as follows : -6,-6,-6,-9,-6,-9,-5,-5. The average is -6.5. I then thought to start all over and do another set. This time I got: -7,-9,-8,-8,-11,-11,-10,-8. The average is -9.