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This is the main reason I bought a 5D3.
I work on a tripod for portraits and the 5DII and all the other similar systems are an utter pain, there is never a reliable AF point anywhere near the eyes.
The 5D3 is much much better in this regard, better in fact than my 1Ds3 as I now have more points to select from even than that.
The 5DIII is a significant upgrade from the 5DII in every way, except IQ. It will certainly solve this issue for you.
Yes and in addition, I set the AF point based on orientation of the camera. If I flip the camera from landscape to a portrait orientation, the default AF point will go automatically to whatever AF point I selected to be more convenient in the portrait orientation.
Plus, you can register two different AF points depending on which way up the camera is in portrait orientation, shutter button side up or down