A couple of things, remember the camera is not 'tack sharp'. The lens is. Of course a better camera will make a great lens better. But the better camera is not going to make a average lens better.
The first version of the ef 100-400mm is an average lens. I suspect that is as good as it gets at that distance. The resolving power of any lens goes south at that kind of distance. Unless the subject is huge. Like the Moon.
Now that is not to say you can't do some things to help it. That also depends on your technique. So first suggestion is, get closer. Make very sure you don't mis-focus. For that shot use only the center focus point. And of course the extreme cropping is a no-no. Like Scott said the lower ISO numbers are going to be best but I doubt you can see any difference between 100 and 800 on a 5D Mk III. The 100-400mm needs to be stopped down at least one stop to be at its best.
MFA at that distance is not likely a big factor since DOF will increase (unless you missed your focus point). And you know never use any filter on that lens. It simply doesn't have the IQ to give up. It goes without saying don't use any tele converters either.
Big always do point is use the hood. All the time. Every time!
Now about your 24-70mm? Is it first version or second? Can you show me a sample from it that isn't sharp? Also don't strip the EXIF from it. The second version of that lens is one of the sharpest lenses I have ever used and used. The first version is just an average lens. Don't get me wrong here it is a good lens, used one for years, it just isn't in the same league as the new version.
EB
EOS 1D, EOS 1D MK IIn, EOS 1D MK III, EOS 1Ds MK III, EOS 1D MK IV and EOS 1DX and many lenses.
