Unless your new classical mechanics predicts the outcome of an experiment that other existing theories cannot predict, and that prediction turns out to be true

Unless your new classical mechanics predicts the outcome of an experiment that other existing theories cannot predict, and that prediction turns out to be true if such an experiment is conducted, your new idea is just another hypothesis. Furthermore, all the real physical quantities come from the fact that we assume space and time to be continuous (i.e., similar to real numbers). So your hypothesis boils down to the claim that space and time are discrete. And that is not new. Plenty of people have proposed that hypothesis, and the idea of planck length and planck time are conjectured to be the smallest units of space and time. But the two values are of the order of 10^-35 m, and 10^-44 s, respectively. This is way below our ability to prob smaller length and time scales. And to the extent that we have been able to prob length and time scales (roughly 10^-15), space and time appears to be continuous. Finally, when you're giving up continuity in any sense, you're essentially 'quantizing a theory'. So it's no longer a classical theory but a quantum theory. We have already quantized energy (quantum mechanics), as well as physical fields (quantum field theory), and associated phenomena. But quantum (i.e., discrete) space and time are only a hypothesis at the moment.