DPReview’s initial tests of the a7s III video performance are just coming in, beginning with the rolling shutter measurements, and the findings are pretty spectacular: below 10ms in all modes! 4K 60p/30p/24p measured just 8.7ms; 4K 120p (one I plan to make a lot of use of) only 7.7ms and 4K Steady Shot Active (60p/30p/24p) 7.8ms. This extraordinary achievement demonstrates the decisive advantage of fewer, larger photosites (unlike the tiny cellphone pixels found in the R5), along with benefits such as improved signal-to-noise ratio, greater dynamic range and increased low light sensitivity.
Considering the phenomenal rolling shutter figures, thirteen stops of dynamic range, stratospheric low light sensitivity, full pixel readout 4K 120p, improved color science, excellent autofocus, manageable codecs and file sizes, updated ergonomics and the widest selection of native mount lenses of any mirrorless system, the a7s III a very compelling package. I just hope my dealer gets them in soon!
The Daejeon Chronicles 
The beast in a small package just before the cinema cameras.
Finally and it’s normal, sensors made for a given resolution allow to avoid problems in video: less rolling shutter, less pixel binning/line skipping, less computing, less heating, more time to record.
In hybrid full frame, as you said, the A7SIII is the only candidate.
However, the IBIS is far to be perfect and sometimes create weird effects in the corners (can be seen in the making of “Trust yourself” from Olivier Schmidt). The same for autofocus.
This can affect the image rendering.
I usually use a gimbal. ☺️
The good point is that autofocus (and IBIS ?) can be disabled if needed.