For this kind of situations 1Dx and D5 are built. Fast af, build like a tank, 16fps (or 20fps in live view), a buffer that almost never be filled...
What's interesting for me at this moment by looking at the videos about 1Dx Mark III are the live view specs. It seems that Canon has 20fps with both electronic and mechanical shutter in this camera. This means that they already have the technology for their next flagship mirrorless. Sony A9 II has 20fps with electronic shutter and only 10fps with mechanical shutter. And that touch af button seems blazing fast compared to the traditional joystick.
2020 became interesting in terms of mirrorless for Canon.