One way in which I believe a reconstruction would aid the investigation, is that it would confirm or exclude the possibility that the man Jane Tanner saw was the abductor
As I see it, if the Man Jane saw was the abductor, then he had, at most, a three minute window of opportunity
In a reconstruction, a policeman would play the part of 'the abductor' and whether or not it was possible for him to have entered the apartment, opened the window and shutters, picked up the sleeping child, made his way around the wall and through the car park, and be crossing the road just as Jane was reaching the top of the hill, would be demonstrated
If it was proven to be possible, then the investigation could conclude that the man Jane saw very likely was the abductor
If it was proven to be impossible for the crime to have been committed in that time-frame, then the investigation could eliminate the man Jane saw as a possible abductor, and concentrate on the other 'windows of opportunity' that an abductor may have had ( at some point later )
Wouldn't that be of benefit ?