first off all it's nice to see that there are indeed photographers on this site not only gearheads.
The images on your flickr stream are fantastic! I wonder how many years it will take me to get on your level...
About the focus issues: I use a pretty similar combo - 5D3 and 500 f4 L II and I did not encounter said issues. I'm sure that AFMA has nothing to do with the problem, since you said that only backlit images are affected. As others suggested using some kind of AF point expansion will pretty surely do the trick (I always go with 4-point expansion when necessary). Single point on a black eye sounds not very promising.