Sometimes I shoot ibis, though personally I prefer curlews, but I don't think the camera has any ibis inside of it.
Nah but seriously, the camera body doesn't have stabilisation, but my long lens does. I've finished my first pass through the photos in the time between posting the OP and now, and yeah I think you're right that especially when I'm zoomed in all the way, a faster shutter speed would help—I'm a little more confident now that some of the blur was shake.
It could also be a “get good” situation where you just have to anticipate a little of what might happen
Oh 100% this was part of it. Reviewing my photos, a lot of them it's very noticeable that had I hit the shutter a fraction of a second earlier, the photo would have been better, from a composition/subject perspective, and I'm sure anticipating where the action will go so I know which subject to try and set the autofocus to be focused on would help even further.
But right now I'm struggling to get the camera to stay locked on focus to a subject even when I do know I want to be focused on them. I believe Nikon's "3D" AF is a kind of tracking mode, and from my reading I think 9d (or "9-point dynamic-area") and group-area might be tracking of some form, too. But they're distinct from the face- and subject-tracking AF modes that are available only in live-view (looking at the display screen), when I'm mostly shooting through the viewfinder because it's much, much more responsive. Even if that wasn't a problem, I think the need to actually select an object to track and keep changing which subject would put it back at the start. Still a "get good" situation, but more about getting good with understanding camera features and using them appropriately, rather than just with the more creative side.