Can our Greek friends provide any insight on this point?
Another specific point on which our Greek friends might help would be: "Is there precedent in Greek religion for a god dying (or choosing to die)?
I don't think that would be determinative of what Epicurus thought, because he clearly rejected many/most of the common attributes of gods, but if there are examples of such things (in Homer especially?) then that might be evidence to add to the discussion.
We presume that gods must be omnipotent and omniscient due to the influence of the major world religions. Is it possible that "immortal" and/or "eternal" is another attribute that we should not presume Epicurus accepted?
I have an open mind on this issue. I also have an open mind on whether a Epicurean gods are "eternal" (no beginning or end) or simply "immortal" (no end, but having a beginning). And that would have to be answered both for an individual god as well as for "the gods as a group"