Daniel, a key difference between the two philosophies that jumped out at me now that I've read your above post more carefully is the concept of moral responsibility. Specifically: "it is everyone’s moral responsibility to increase the pleasure of every person (including themself) while relieving their pain."
To the best of my understanding, moral responsibility is excluded from Epicureanism. In it's place is PD5: "It is not possible to live pleasantly without living prudently and honorably and justly, [nor again to live a life of prudence, honor, and Justice] without living pleasantly. And the man who does not possess the pleasant life, is not living prudently and honorably and justly, [and the man who does not possess the virtuous life], cannot possibly live pleasantly."
So as Epicureans we try to live prudently, honorably and justly because living this way minimizes our pain and maximizes our pleasure. There is no moral responsibility to anybody else involved. The end result may possibly be the same, but the intention is entirely different. This might seem reprehensible to a Utilitarian, but to an Epicurean it provides clarity, and with clarity, freedom.