Ah, okay, you are panning while hand-holding and not while using a panning tripod.
You mention you are using the electronic shutter. That may cause you a bit of trouble:
https://fujifilm-dsc.com/en-int/manual/x-h2s/menu_shooting/shooting_setting/
scroll down to the Shutter Type section for the notes on shooting moving subjects.
I have heard that increasing the fps does make the focusing sensor work better, because it takes more samples, but I do not know for certain one way or the other.
Just to cover all bases, have you considered using a smaller aperture (higher f-stop number)? Even with zone focusing, too small of a f-stop number will still blur things outside the immediate focus area, which can be tricky to center on a moving object.
Using the idea of shutter speeds twice the focal length should still work, that is what folks did before IS, OIS and IBIS came along.😀