<<After spending some time Adjusting the AF Fine Tuning on my 200-400 on my D4, I got amazingly sharp images all the way across the full 200-400 focal lengths.>>
What concerns me especially with zooms is that the environment that LensAlign and FocusTune images are taken in i.e. almost laboratory conditions. The real world is very different with no fixed aperture, speed or even ISO or focal length (unless using a prime, Where I get confused is where the two environments cross.
For example, I tested my 70-200mm f2.8 and it stated for 180mm it required a fine tune of +15, whereas at 70mm it gave -5!. So, I fixed a flat target ISO test chart and handheld at 70 and 200mm. On checking the chart it was sharp as could expect. The same happened on my 24-70mm with different AF fine tunes massively apart. I think that the difference between the tests was that the LensAlign takes into account discrepancies caused by front and back focus. In contrast my 300mm f4 resulted in a fine tune requirement of -5, so I just left it as when I compare 0 and -5 against a flat target handheld the results were virtually identical.
I too am a wildlife shooter and I feel as I use mostly single point focus (occasionally multi-point 3D tracking) fine tuning doesn't help me. Interestingly, I have noticed no narrow DOF or wide front or back focus problems either.