On closer scrutiny of images of the stone disc and thongs, it appears that my model may not be totally correct.
It looks like the 9 thongs are simply held in place by tension of the the central ring and not tied to it as was shown in my model. In this case, each end the of thong would have been tied around the animal.
I guess the only way to know for sure would be to fly to Italy and have a look. But that’s not in the cards at the moment!!! Maybe someone who has seen this item can let me know.