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I agree that your shutter speeds should have eliminated any blur from camera shake at those focal lengths. However, it looks like your auto focus just missed a bit, and you probably should have stopped down to f/8 for both deeper depth of field and I suspect that your lens is probably sharper at f/8 as well. Finally, I wouldn't use AF-S for a moving subject unless it is only lateral movement that wouldn't change the distance between you and the subject.

Having Fuji, Olympus and Sony, I would advise you to try an Olympus body: its IBIS technology is fantastic and would allow you to put that "extra-shake" behind your concerns. Or, if you really want to go Fuji, I guess you would be very happy with a 2nd-hand X-H1 (I had one and replaced it with an X-T3): it is heavier and the IBIS is also great. But I'd check the Olympus before anything...

These images could not be sharp for a number of reasons. There is an easy way to check. Find a room with plenty of light, no wind, and put camera on tripod. Get one of those charts with lots of lines and colours - like a projector focussing chart - and take pictures (using a cable release or self timer) of it at various distances and apertures. Then you will know.

X-S1