Excellent stuff Elli ---
Before I forget where I was going originally, let me put this back out there again. Did the Greek gods feel pain? Did a Greek god ever choose to die? Is it possible that an Epicurean god could die if he chose, and feel pain if he chose, but simply chooses not to and has the ability to carry out that choice?
I think the practical application of that question is as above: "What, in Epicurus view, did "the gods" have that humans cannot experience? Is the only or main difference that the gods can experience pleasure longer and with more variation? Our variation is limited by our lifespan, in that we cannot control our atoms so as to self-renew our bodies. The "gods" can do that, and thus have unlimited variation.
Is it possible that this perhaps the main difference between us and the Epicurean "gods"? That may not be at all true, but if it were, certain comments like the "gods among men" comment would be more understandable.