Jeff, the new details you describe totally change the situation. Moving the Start to a new location, as described in my initial response, would use the same cert number. But, since the moved Start is not replacing the original Start, means this is a new course, and needs to be measured and certified as a new course. Add to that, the Finish has also moved, and there is no question that the new course can't claim to be an altered version of NY10015JG.
Just because two different courses share most of the course, does not mean that the two are the same, certified course. Start and Finish are different, and when the new map is created for the "adjusted" course, I would be the new race director does not want the old course name on his map.
Hope this clarifies. I initially thought that only the Start was moved, the old course would go away, and it was for the same race. Sorry I misunderstood.