David,
congtars on starting this amazing series.
I think you already know the article by Melanie Grunow Sobocinski:
Ludi Saeculares Visualizing Ceremony.
Starting from the observation that
RIC 623 is much more common than the other AE coins of the series, she deduces that only this coin was minted in large quantities and circulated throughout the territory of the empire.
On the other hand, the others were perhaps distributed to the public during the celebrations, since they would have been found only on
Italian territory.
Alberto