I need to check the texts but do I remember correctly that Epicurus didn't necessarily write against logic so much as rhetoric?
I think the answer to that is once again "Logic" has to be defined. Saying that he attacked "all logic" is almost certainly overbroad. Lucretius talks about "true reason." The real target is probably better stated as "logic based on nothing that can be verified through the senses." Use of the term "abstractions" is probably overbroad, and "abstract logic" isn't clear enough.
So I do think that Epicurus' target was definitely against more than "rhetoric" and there you have to consider his comments on poetry.
The work "Against the Megarians" seems to be part of what we 're talking about.
And you'll find what I am suggesting to be confirmed, with much more detail, in Delacy's comments to Philodemus including:
Appendix 1 - Sources of Epicurean Empiricism
Appendix 2 - Development of Epicurean Logic and Methodology
Appendix 3 - Logical Controversies of the Stoics, Epicureans, and Skeptics