The gods would have no more need of infinite lives than a mortal would,
Just to pick a random comment out to bounce off of ---
They would have no more need for infinite time in order to enjoy "complete pleasure" or "pure pleasure," but they would be able to do so for "longer," which would in itself be desirable, just like it is desirable for us to live pleasurable lives longer. We aren't missing anything by not living on, but that doesn't mean that living on longer is not desirable. That's the common sense way we live our lives - we want to continue living so long as the expectation of net pleasure can be achieved, and I don't see why that consideration would not apply to "the gods" or any other living thing.
And as for the "necessity" of all things eventually breaking apart, even our world, it seems to me that the texts are saying that this is a "necessity" only because the blows from the outside eventually overwhelm the structure of the living thing. Seems to me there is no reason to foreclose the possibility, and indeed I think it's likely, that ways can be found to continue to replace the lost / destroyed structure indefinitely. If the "world" is in danger of collapsing, then rational beings would leave the collapsing one and go to one that is not collapsing.
I know some of us are shying away from these conclusions, but I don't think that Epicurus would have shied away from them any more than from his other radical conclusions. This is a subject we need to examine much more closely but I see no supernatural force or "necessity" that any particular object must be limited to a set and particular life span.
The problem with "immortality" is that we don't see how it can be achieved naturally, but then we couldn't for a long time see how men could fly or go to Mars. I doubt there is a conceptual difference between going further and further out in space and extending life spans longer and longer. The issue is simply finding ways to replace the structure, like making sure that there is an endless supply of water and channeling it to continue flowing over the waterfall.