But! This is a very fast little bugger and I had to prefocus on the opening of the whole. When the head of the bird appeared in the opening, I would fire the full 12 fps on the 1DX, which gave me one frame with the bird still in the hole, one in the air and one of its tail feathers.
Question: How should I set up the AF system to be able to track that movement? Is it at all possible?
(600mm f4L IS II, at 1/4000s, F11, ISO4000
Seems like you got the shot you wanted! I think most of us (if we are honest) are still learning the AF system on the 1D X, there are just so many possible combinations and a lot of them work for multiple situations. The last int. sporting event I was at, I was having a beer with a guy that was also shooting a 1D X together with the 400 f/2.8 ii and I asked him about his AF set up to compare it to mine. Turns out we had both messed around with three different of the 6 AF cases/scenarios but not one of them was the same!! Who was right and who was wrong? No idea, but we both got the shots we needed.
I do not shoot birds very much, but considering you were at f/11 I would probably have gone with 8-pt Expansion and taken it from there. After that it is a question of finger speed etc. As for the case, I may have reduced the lock on so that AF could change more quickly from the bark of the tree to the bird, but beyond that I am not sure. I do feel this is a scenario where back button AF can also help. Am sure you use that already right?
Anyway, there are people here at CR that are far more talented and knowledgeable than me when it comes to shooting birds, so hopefully they will have some input I can also learn from.