A good thought, but.... 60th of a second was the minimum, and only for some shots with the 16-55. The issue was more with the 50-140 which just seemed unable to lock onto faces at times, and shutter speeds with that lens were 125th.
As for C setting - I had no idea about that, I didn't even know the X-H1 had eye or face detection...!
OK, in case it helps here are two consecutive images, heavily cropped obviously, 2500 ISO, 125th of a sec. I know the shutter speed is possibly a bit low, but 90% of the other pictures are ok.
View attachment 321025View attachment 321026