As I understand it, thus rituals do not move the gods, per se, but rather may bring us in communion with a portion of their divine light.

Right, Sallustius says that the Gods are active rather than interactive, and I follow Sallustius argument about the purpose of worship and prayer being to get us on Their wavelength. Still, I wonder if some amount of all this is to befriend Their dæmons? John Opsopaus has a succinct summary that apparently matches my thinking:

As a consequence of Their intermediate nature, Daimones serve as Mediators between the Gods and us, and They convey divine Providence (Pronoia) into the sublunary realm. In particular, They interpret the Gods' wishes for us and are the agents of divination, oracles, and rituals. They are ministering spirits who care for people, and are often called Savior (Sôtêr). (Recall that daimôn is from the Indo-European da-, to provide.) Many rituals are directed to Daimones (who have feelings and can be swayed), and They are thereby convinced to mediate with the Gods on our behalf.

According to Pythagorean doctrine, the Gods reside in the Noetic Realm, the world of Platonic Ideas, so They cannot relate to us as individuals, but only as representatives of the Idea of humankind. The Daimones, however, being intermediate, participate in both the Ideal and material worlds, and so they interact with us as individuals. They know our personal and family histories, our personalities, and often our thoughts.