You are in the exact same position as me with almost the exact same camera requirements and same needs for what the camera will be used for, except I need it for Time lapses also. So I will be interested to know your final decision. I also suspect like me you also want to pick 1DX2 but see the superiority of the A7R3, which is probably what is stopping you or making you hesitate pulling the trigger on purchasing the 1DX2
I personally have decided I will almost certainly be purchasing the 1DX2 with some L zooms, 16-35 2.8, 70-200 and 24-70. I'm sure you know as you have stated a few of the Sony advantages over the Canon, so I will list the ones that have swayed me towards Canon.
1. Better Colour Science. Less colour processing in post. I do find the look of Canon so much better.
2. Better, buttery 120p. Correct if I'm wrong but the Sony 120p is of poorer IQ and not as smooth. Also I think Sony is down sampled?
3. Cheaper lens, the L is still just as good to my eye, despite what DXOmarks rate the Sony at.
4. Weather sealed. There are tests showing the A7R3 and Nikon(D5 or 850, I forget) failing compared to the 1DX2. i.e. its a tank
5. it's a tank
6. More FPS
7. Better menu system
Cost wise, the 1DX2 is more expensive, but the Sony G master lens negate any financial gains. And you will be buying more lens later. I will also note that it is incredibly hard to find anyone selling their 1DX2 second hand. I'd have to conclude anyone who buys one just doesn't look back.