In regard of - "The dancers are in white against dark green curtains, this provides very good contrast, an easy target for AF" - you think 6D outer AF point(s) be able deliver same sharpness?
I'd expect my EOS-M with adapter and EF lens to lock focus on that kind of contrast. Seriously. This isn't a pissing contest, it is just a measure of contrast, there is a huge amount of contrast between the dancers in white with stage lights on them and the dark green light absorbing curtains, at iso 8,000 you have over 8 stops of dynamic range, some of the white dresses are blown and some of the footlights and orchestra pit black, that is a contrast ratio in the order of 300:1, an easy target for AF. By contrast (no pun intended) the 6D AF center point is rated down to -3EV, a contrast ratio in the low double digits.
Again, this is not a judgement of the images, purely a deconstruction of the task the AF was asked to perform. I am not suggesting for one second that the off center AF points in the 6D can come close to the performance of the 5D MkIII off center AF points, just that the two posted images are not good examples of where the differences would show up.