There is a brief space in between the stimulus and your reaction, therein lies the spot where you can change.

You have stated the mechanical world view fairly well, and reasoned out free will and moral agency from it.

However, I do not agree with your world view at all. I have had too many personal experiences that say that the mechanical physics world view is bunk. The best I can say is that you have no idea what time is. If you think that time is linear, you have no idea of what time is.

Here is a piece of data that really is a sticky wicket.
An open brain surgeon did some studies where he would prick someone's finger and record how long it took them to respond. Then, he would stimulate the area of the brain and record how long it took to respond.

His thinking was that it would take longer for the signal to travel up the arm and reach the brain. His findings were the exact opposite. The subject felt the pin prick almost instantly when it happened. And the subject experienced a delay when the section of the brain was stimulated. So, if it takes time for the signal to propagate along the nervous system, the signal has to travel back in time.