Thanks guys.
Well, as to the use of AF-C with the X-T10 being masochistic, hek, I've only sliced both wrists twice and attempted to hang myself once. Not bad, considering!
As expected, using just the shutter button locks in the exposure (on AF-C); hence, as you said, Doug, back-button focusing is better here. My problem was that even using back-button focus I couldn't get the AF-C to work but only once in a while. And then I figured out why.
I wasn't just trying to track things, I was also trying to move the camera from it's initial focused area to another area to see how the focusing would react. The camera wouldn't respond most of the time, which, okay, I get it: "Hey, give me something to track or shoot in single focus, idiot!" Got it.
But even when I try tracking, it's a bit of a task (part of that masochistic stuff you mentioned, Doug). It works, but it is definitely limited: single-point focus, for instance, seems much more comfortable either tracking object that are coming somewhat more so in or away from my direction, or objects moving fairly slowly.
Understanding this now, I can see what I'm in for, and that's fine. I'll deal with it: I'll buy an X-T20 and then carry the X-T10 along just so it gets more and more jealous as time goes on. Let's get sadistic!
Hey, thanks again, all. I appreciate the input. This camera is a bit of a change from my Nikon D3200, but it's a cool little camera.