No matter what action the "deterministic rules of science" prompt, we can always choose to do otherwise, if only to show that we CAN. That is free will in action, and it is nothing more than an ability to act on our feelings or not. Why you think we need to invent a soul to explain the ability is obvious ... you are trying to shoehorn your "God" into the equation, but it won't work - it's superfluous.
I agree with you last point, Len, regarding Alan's 'souls' theory and also I accept that in day-to-day living we operate as if our choices are free in terms of, say, choosing 'x' rather 'y' in getting through the events of each day.
However, I'm not sure that beyond viable mundane choices 'free will' isn't an illusory oxymoron of sorts, since 'free' implies no constraints and yet naturalism imposes some by default, and 'will' operates within those constraints relating to my current and preceding circumstances and my future options and of course the impact of external factors outwith my control.
In that sense I'm not sure I really have 'free will' in that constraints apply whether I like it or not and I am exposed to events and influences I can't control and may not even recognise or fully appreciate.