There has been an enormous amount of discussion in the past in regard to the theological aspects of Epicurean philosophy. There is, as of this moment, no consensus of opinion in regard to that subject and it continues to remain inconclusive.
However, this post is not focused on that generalized subject, but rather on the gods of Ancient Greece and Rome and the use of them specifically as "role models" either aesthetically or in a practical manner for an Epicurean.
The gods of Ancient Greece and Rome were derived from common Indo-European deities. These deities, such as Zeus, Aries, Athena, Poseidon etc., have their counterparts in the ancient Indian, Iranian, and Celtic/Germanic pantheons. Almost every deity has a foreign counterpart that fulfills the same role. So the only particular reason why an Epicurean might adopt the specific Greco-Roman versions of these polytheistic deities would be for culturally aesthetic purposes.
Much of what what we know of the myths and legends of the gods come from Hesiod and Ovid. It is clear that the known Greco-Roman myths derive much of their character from Mesopotamian, Levantine and Hittite archetypes. Some examples are: Cronus castrating Uranus, Zeus battling Typhon, the deluge of Deucalion etc. Like their foreign counterparts, the Roman and Olympian deities are far from an Epicurean ideal and do not represent the Epicurean archetypal deity.
These deities are described in the Theogony and Metamorphosis as having identical emotions as mortal beings. They interfere in human affairs constantly and are petty, wrathful, cowardly, amorous etc. The latter emotion of being amorous is particularly prevalent among some of the gods including Zeus, king of the gods, who is polyamorous. Zeus had multiple divine relationships, but worse Zeus was also a seducer of mortals and was described as taking the form of a Swan to seduce a human female and even worse he is described as the pederastic abductor of Ganymede. There is no other way to described the latter except as debauchery. This is only one example, there are many, many more throughout the myths implicating many of the gods.
So where does that leave the Epicureans? Hopefully far, far away from the traditional Greco-Roman deities. The deities are far from what is described in PD.1 as they interfere constantly in human affairs and are exceptionally emotional, often troubled by minor offenses committed by mortals.
Should modern Epicureans be partnering with neo-pagan reconstruction religious groups? Or promoting the aesthetic ideals of Greco-Roman religion?
In my opinion, I say emphatically NO. Such a relationship would be an endorsement of superstition and it contradicts the core principles of Epicurean theology. In my opinion there is no room for Zeus or Jupiter in modern Epicurean iconography or thought as it would be the same as glorifying Indra or Ba'al of foreign pantheons. It would simply be hypocritical and a denial of PD.1.
So the question becomes, what can modern Epicureans use for an aesthetic image for their specific philosophic deities in lieu of the debauched Olympians?