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I think you are correct in your subject motion thought. At the slower shutter speeds any little input, a thermal, a little aileron or rudder, will cause that. You can tell the difference between camera motion and subject motion by looking at the grain sharpness, if nothing is sharp, the problem resides at the camera, if the grain i sharp, but he subject appears a bit "3D-ish", then it's the subject.
Sorry about the politics, I hate that, but it pops up everywhere. The older I get the less patience I have for it. I'm getting to the point where my default is to quietly distance myself at the first hint. I realize that, because my opportunities are plentiful, that's a luxury not everyone has, but I find walking away is like cutting off oxygen to a fire.