I think the Paradox suffers from a lack of understanding of Good and Evil.
Here are some moral dilemmas:
25 Moral Dilemmas
It is easy to create more. In the face of all these moral dilemmas, how do you discern what is "evil" from what is "good" using logic alone? You can't.
Would you be convinced that someone is not good because of his decision in a moral dilemma? I hope your answer no. And that's why the entire argument is nonsense. It's just a glorified moral dilemma.
Let's follow where exactly the argument breaks down:
1. Evil Exists.
Answer: Yes.
2. Can God prevent Evil?
Answer: Yes and No.
Some Evil is preventable.
Moral Dilemmas demonstrate that the answer is not an absolute yes or an absolute no.
Some Evil can be unpreventable. Some Evil can be preventable.
If you want to say that God can prevent Evil that is not preventable because He is God
(in other words, you interpret "all-powerful" to mean He can break logic),
then you have to concede that you can't use logic to trap God and thus the Epicurean argument fails before it begins.