So some version of gods are possible given these conditions, even probable, but are not required.
Lots of these words have multiple meanings but to focus on "required" -- required for what?
Epicurus and Lucretius are very specific as to the need to avoid "thinking unworthily of the gods" as a means to the most happy life - for example here in Book 6:
Unless you purge your mind of such conceits, and banish them your breast, and forebear to think unworthily of the gods, by charging them with things that break their peace, those sacred deities you will believe are always angry and offended with you; not that the supreme power of the gods can be so ruffled as to be eager to punish severely in their resentments, but because you fancy those beings, who enjoy a perfect peace in themselves, are subject to anger and the extravagances of revenge: and therefore you will no more approach their shrines with an easy mind, no more in tranquility and peace will you be able to receive the images, the representations of their divine forms, that form from their pure bodies and strike powerfully upon the minds of men: From hence you may collect what a wretched life you are to lead.
And if "which version to accept" is the issue, then that is a matter of adhering to clear Epicurean texts, or going one's own way on them, since no one has formed a "club" with a "membership requirement list" requiring that any particular version of divinity be believed.
My personal bright line is mainly to rule out of court any version of the position that "Epicurus said things things because he was a hypocrite, just to save himself from the fate of Socrates." Because at some point if someone doesn't respect that the Epicureans were attempting to be honest on something as basic as this, on which they made repeated clear statements, then that person really has no sincere interest in being part of a group that respects Epicurean philosophy.