That makes sense. Which makes it all the more puzzling why it was not done.
I would have thought that part of the point would be the media interest - pubicising the event may have triggered memories in peoples minds and could have led to further leads.
Not in Portugal as the concept of a reconstruction / reconstitution is to assess potential guilt of those summoned to take part as opposed to a public appeal for potential witnesses.
One possibility is that they really weren't aware that reconstructions in other countries could be used as an appeal and that therefore a reconstruction would have intimated that the group were suspects. However, it could have been handled differently, as I suggested earlier. They could just have wheeled out the valiant de Sousa to state that it was to pinpoint when she could have been taken.
The other possibility is the fact the coordinator was an arguido himself in the Cipriano case (which involved a so-called "reconstitution" in dubious circumstances as virtually the only "evidence" on which they were convicted, not to mention the torture), and might have drawn unwanted press attention to that case. Particularly as it also involved a missing child not that far away, with an abysmal investigation, and no evidence as to what actually happened to her.
Amaral moans about political interference. However, IMO, it doesn't take too much to work out what the diplomatic exchanges were actually about...