The reasoning on this is well thought out, but logic based on assumptions that are wrong produces wrong results. It of course pre-supposes that there is no God and then addresses the problem from a human point of view.
The flaw in this reasoning is that God is billions of years old and he created all things- certainly he can manipulate atoms and sub-atomic particles to make what he wants happen. If YOU could control matter and energy on this scale, would it really be that hard for you to make the sun stand still? Or extend the light for that day and make it appear that the sun stood still?
Just because this is impossible for man it does not mean it is impossible for the Creator. Just because you personally have never seen a miracle doesn't mean they can't/haven't happened. And advanced science can be a "miracle" to someone without the equivalent technology.