If it's any help...
Since writing the article back in the summer, I've done a lot more action shooting with the Sony RX10iii and am very pleased with the results. Just to qualify my comments, I've shot field hockey and soccer outdoors and volleyball and basketball indoors, so, both "fast" and "slow" sports under very different conditions. In all cases, the number of missed shots increased compared to my D800E, but I also captured enough excellent shots to not worry about the missed ones (I'm not shooting for Sports Illustrated, after all!).
The only real weakness I can see with the RX10iii is trying to follow birds in flight, but that is also my own shortcoming in technique. I find that in continuous focus, I irretrievably lose focus the second the bird veers out of the focus box. The D800E does a much better job with 3D focus and all (as it should do for considerably more $).
I must admit to being intrigued by the Olympus set-up Kevin reviewed recently. That 12-100mm lens is sure tempting combined with a sensor twice the size of a 1" sensor. But then I discovered the lens alone is the same price as the Sony RX10iii; I'll stick to the Sony, thanks.
Lastly, I've been using the Sony at ISO 64 and am greatly enjoying the results. I've also had great success with maintaining sharp details even when using f/11, but only on a tripod. Diffraction (yes, not refraction!) clearly becomes an issue at f/16.