Good issue for thought. My first thoughts:
the perhaps downplayed it because "guilt-driven" morality was mostly framed in a religious context like with Stoic and Platonist talk of violating divine reason and "feeling of guilt" not being universal enough for him (obviously psychopaths and masochists exist)
I wouldn't think the universality or lack thereof would have been as central. More central would be - as you mention - the falsity of the religious / divine reason context of "guilt." I don't think Epicurus would embrace something he knew to be false regardless of its alleged practical benefits. And Diogenes of Oinoanda makes pretty much the exact point that the threats of religion do not in fact work out in practice.