I have the 70-200 f2.8 IS and the Canon 2x II extender. I have to say that I was quite impressed with both the IQ and the speed of the AF. To be honest when I bought the extender I really was expecting the worst, but ended up being very happy.
Just got the Kenko 2x TC DGX. On 5D MkIII, it ONLY works with 70-200 II, not anything else, which I expected since my Kenko 1.4x only works with 70-200 II as well. Kenko can keep denying compatibility problems with 5D III and put their head in the sand, but problem exists.
On 70-200 + 2x TC, probably cropped out 80% of the photo. It was at dusk, so iso2000.

DZ3C3817 by drjlo1, on Flickr
hmmm all my lenses seem fine on my new body with my kenko stuff, on the first body i returned none worked, I think its body dependent, do you have any other wierd focusing problems? my new body has a 3 in the 6th digit my first one was a 1