I have been using 1 series DSLR bodies (currently 1DX III) with the EF version of the 400 f2.8 lens for several years and the lens acquires focus VERY quickly. I have tried R1 bodies a couple of times but have not been motivated to switch yet so I don't have a lot of familiarity with them.
With the 1DX III, I leave the camera AF set for focus priority instead of shot priority because I see no use in having an out of focus image but I have not found that to be a hindrance in capturing rapidly changing action.
Are most of your O-O-F shots occurring when rapidly switching between two places on a field (i.e. the QB release of a bullet followed by the reception 30 yards from the QB)? If so, what you may be running into is the slight amount of additional time it takes for the photographer to follow/frame the action using a longer focal length lens and the "cure" is to force yourself to immediately switch your view to the receiver the moment the ball leaves the QB's hand.
If the O-O-F shots are occurring in a sequence where you are following the same action (i.e. football running back or a soccer player working the ball through the box in soccer to get a shot) then you may want to consider how you are using/defining the AF area. When I first got my 1DX III bodies, it was interesting to watch it identifying "targets" using its full focus sensor area however I quickly found that limiting to a few potential points either dead center or lower center of frame (depends upon sport) works better for me. The various "cases" Canon has available to provide different AF personalities are excellent but you and the camera are still a system assisting each other and although the technology Canon has put into its AF system is incredible it still works better as the photographer's very capable partner. For me, it also keeps me mentally focused on the action keeping the key part of the play properly in frame using that smaller set of AF points.
At times, you will want to make strategic use of the AF stop buttons located in a circle around the lens. For example when shooting corner kicks in soccer, I focus on the keeps position and press one of the AF stop buttons and then follow the play through the camera even though the image isn't in perfect focus. Using this strategy, I have the lens pre-focused on where the action is most likely to happen and I can then let it snap to perfect focus instantly when the action starts near the prior selected point. I shoot with two bodies and for that reason I do not like having AF on a separate button, any additional finger placement creates another delay when you are switching bodies during a fast moving play BUT I do program the AF button on the camera body as an AF STOP button for the rare occasion when I want to have AF stop with a lens that doesn't have the AF stop buttons. With the big white primes, those buttons are perfectly placed when using both hands to manage the camera system.
Rodger
EOS 1DX M3, 1DX M2, 1DX, 5DS R, M6 Mark II, 1D M2, EOS 650 (film), many lenses, XF400 video
