I have to agree that it seems to defeat the point of buying a 5DIII, if you are going to focus manually, the AF system is so versatile and accurate it locks on fast and hangs on like a limpet, it just doesn't miss (I might on occasion, but it doesn't).
I am not saying this because I have never focused manually, I grew up doing so and always swore blind that AF was never going to be as good at focusing as I was. When Canon went to the EOS system I stuck with my old FD SLR outfit, preferring to focus manually and not seeing any reason to change to the new AF oriented system. When I eventually went digital in 2004, I had no option as everything was AF based, so I switched to EOS with a 20D, then a year later the new 5D (the original one). These taught me that, much of the time, AF was now at least as good as me and could just snap into focus at a tap of the button. Sure, the 5D had flawed AF on the outer points in low light, but the centre point with assists was great. Outside of its comfort zone, using outer points in low light, I would often find myself tweaking the focus manually however. I believe the 5DII has essentially the same AF system as the mkI.
Since getting the mkIII (almost two years ago) I have never felt the inclination to focus manually once, it just nails focus time after time. I know that this isn't quite an answer to your question, and doesn't help where your Zeiss lenses are concerned, but the mkIII has made me an AF convert.
However, you did mention using the AF for sports, so I assume you have some AF lenses. My suggestion would be to keep the mkII for using with the MF lenses you have and use the mkIII for sports, where it really shines with its AF.
I realise that there is a very large amount of personal preference involved in such things though, so this is more of a comment based on my experience with the MkIII, and I don't have experience using the MF screens in the DSLRs. (I do know the difference a good MF screen and long throw focus ring makes to focusing manually, but I left that behind when I went digital).