Nice analysis! As you mention, it's really about storytelling, first and foremost. So the decisions made were taken to enhance the flow of the story for the viewer. Plot holes only become a serious problem when they jeopardize the viewer's experience in the moment of watching the film.

Another way of looking at some of these issues, mind you, is to question the perspective of the camera when we're in The Matrix—i.e., "The image translators work for the construct program." It's at least an option to interpret it as suggesting that, when in The Matrix, the visual logic and flow of events is engineered to compel or convince a human viewer. So yes, there are distortions of logic, but they're deliberately designed to keep us engaged in what we're seeing—basically, not to "reject The Matrix". Haha! So Bluepills don't see the body jumping because the visualization of it is only intended for the camera. I mean, that's obviously "true" of the film itself, so why not of the (limited) omniscient camera perspective in The Matrix itself? :)