Akinbo,
Thanks for reading my paper. You are of course correct that the geometric point is a mathematical fiction, as are infinity and other mathematical concepts. Math is an abstract representational system. Math is not physics, although the two have been conflated by our observer-based measurement models (Relativity and QM). The facts clearly demand the hypothesis that space is a substance, so the task of a theoretical physics is to understand that substance and its role in all phenomena. We now know much, much more about the physical world and the evolution of complexity than did the Greeks, Newton, Leibniz or Einstein. Space must have some smallest parts, but I think that they bear little resemblance to Leibniz's monads, which is why I did not use that term. We cannot proceed as did philosophers of old with abstract speculations about the elements of space. We need to instead look at the known phenomena and see what they tell us about space.
I have shown that gravity is most simply explained if Newton's "absolute" space is instead a fluid flowing into matter--its acceleration causing all matter to accelerate with it. We measure its velocity by the slowing of our atomic clocks. See the theory here. This theory solves Newton's action-reaction dilemma-space acts upon matter to resist its acceleration because matter is acting upon space, consuming it as a sink consumes a fluid. You speculate that the spatial elements disappear in front of and are created behind a moving object, that is possible, but because gravity appears to involve the consumption of space by matter and a resulting sink flow, I think it's more likely that when matter moves through space, space flows into and around it. Someday experiments may help differentiate between these two theories. You may be interested in my further speculations about space, its parts and its motions in this essay.
As you are a physician, you may also be interested in my thoughts on the corruption of medicine by pharmaceutical corporations, and the resulting ignorance of natural scientific medicine, including endocrinology. See my practice webpages.
Henry