Blackmagic is only data heavy as long as you shoot in RAW. But so would the FS7 with the AXS-R5. You can still go for ProRes 444 or 422 and still get great images. If you really want to spend money, go for the Ursa Mini Pro or FS5/FS7.
But I think the C100 Mk2 with an Atomos on 10bit 422 ProRes would be sufficient for most productions.
EDIT: Sorry, I just saw that this is 2 months old. Somehow it was shown as a hot discussion...
From looking at the desired shots, I would say that you are best off with a wide lens (about 15-20mm) and a very high aperture (about f8). With that you wouldn't really need to pull focus.
If you want to do more close up and shallow depth of field shots, I would go for the 5D IV and an L Lens (obviously only if you still can change the camera). I have heard of mixed results from the a7S Line when it comes to autofocus on objects. The face tracking seems to be great, but not so good for stuff like cars. The 5D IV would be the safe bet.
Here is an alternative technique you might consider: https://www.youtube.com/watch?v=sTfG8puY_mI
I haven't used it myself, but judging from watching it, it should work.