FWIW (and bearing in mind the replies since this post) I was on tenterhooks waiting for the 5D3 f/8 autofocus update, and swapped from the 500+1.4x to 500+2x without looking back. The extra focal length is almost cancelled out, but not quite, so it's worth it.
Hmm....I'm not sure it is possible for a 2x TC, even a bad one, to cancel out the benefit of the extra focal length. Subject size in the frame is the square of the ratio of the focal lengths. In your case, you went from 500mm to 1000mm, so your subject quadrupled in size in the frame ((1000/500)^2 = 4). There is no way that the TC is introducing so much CA that it is overpowering having FOUR TIMES as many pixels on subject...that would mean your CA was like 13µm in size...which I simply don't believe. Not to mention that CA adds color fringing, which can be corrected, and the overall general softening due to the 2x TC III is relatively low. I mean, it definitely has an impact, but it isn't entirely canceling the benefit of having twice the focal length.
That being said, autofocus is something I'd love to see improved. It works, and that's brilliant - before, I was manually focusing sometimes (e.g. at 1400mm with both extenders mounted), even on birds in flight, but the hit rate was tiny. Any improvement is good, and what the update in April provided was very welcome. But it is inaccurate, as you might imagine - birds in flight are more often than not impossible. I'm torn between frustration and gratitude.
Still the ability to do it at all is awesome, so on balance I am happy.
It's expected that f/8 AF for BIF is pretty much a no-go unless you are exceptionally skilled (and there are a few who are that skilled.) Even with the 100-400 + 1.4x Kenko on my 7D (which is atrocious), for stationary subjects I was still able to AF a reasonable amount of time. That is with a Kenko TC on a 7D...WORLDS different than a 1D X with an EF 2x TC III mounted on a Mark II telephoto. The 5D III runs circles around the 7D+Kenko. It isn't blazing fast instantaneous focus, but it doesn't take minutes either. On the 5D III f/8 AF is fast enough, and consistently functional, which is all you really need for stationary birds, or birds that are slowly moving rather than flying. And that is what f/8 AF is usually used for in the birding world.
Don't expect to be able to f/8 AF for fast moving subjects. It just isn't practical, isn't realistic, and isn't expected (and yet, that seems to be what most people are referring to when talking about how bad f/8 AF is, not even just here on CR...any time I hear someone complaining about f/8 AF they are either trying to BIF, or photograph rutting elk or something of the fast action sort...which is just not gonna happen.)