The same Epicurus asserts that there are four other natural beings which are immortal: of this sort are (1) atoms, (2) the vacuum, (3) the infinite, and (4) the similar parts; and these last are called Homoeomeries and likewise elements." (Goodwin trans.)
Point 3 reminds me of DeWitt's comment about the forces of creation prevailing over those of destruction in the universe as a whole - individual worlds come and go, but the universe as a whole continues forever. To me that makes sense and is a useful point.
Point 4 seems to imply something else that isn't so immediately understandable, at least to me. So this is the same homoeomery that Lucretius argues against "going downward" from our level of existence (that men are not made of little men)? But since we aren't concerned about infinite division on a scale going upward, it is ok to observe that at some level bodies can be grouped together to form larger versions of the same bodies on an infinite or between-the-worlds or "god-level" scale? I think what you are implying Bryan is a grouping of similar particles, perhaps fractal-like - sustainable by flows of similar components, analogous to drops of water forming a waterfall or river or groupings of stars forming a milky way?
The point that even the gods require some form of activity to maintain their deathlessness would likely be a significant part of Epicurean theology, giving us another useful thing to consider as points of emulation. We too have to act properly to sustain our happiness just as they do - there's no supernatural state that "hands it to us free" for men or gods.
Or stated in the way that the death argument is made in Lucretius (if even Epicurus and Scipio had to die, we should not be offended that we too die), then the analogy would be something like: If even the gods must act properly to maintain their happiness, who are we to complain that we must do the same? We should emulate the gods not only in the result of being happy, but also in the process of getting there, with both gods and men acting property to perpetuate our happiness.
Note: I made some edits in the above paragraphs to try to be more clear.