Daniel:
As to "It talks about pleasures and pains, but I guess it never fully encapsulates hedonism." The issue is really "What is hedonism"? The word has no obvious clear meaning -- "Pleasurism," if that is the obvious meaning, and is ambiguous and unclear; Epicurus set out a full and detailed set of beliefs, but "hedonism" is a word to which there is no definite meaning -- that's the main issue.
"That's just my opinion, though." <<< That's really the issue. Epicurus and most Greeks start with the more basic question of "What is the good?" and they look for ways to logically prove that something is "the highest good" before they launch off in pursuit of it, You'll see that in the opening to "On Ends."
"I will start then in the manner approved by the author of the system himself, by settling what are the essence and qualities of the thing that is the object of our inquiry; not that I suppose you to be ignorant of it, but because this is the logical method of procedure. We are inquiring, then, what is the final and ultimate Good, which as all philosophers are agreed must be of such a nature as to be the End to which all other things are means, while it is not itself a means to anything else. This Epicurus finds in pleasure; pleasure he holds to be the Chief Good, pain the Chief Evil. This he sets out to prove as follows: Every animal, as soon as it is born, seeks for pleasure, and delights in it as the Chief Good, while it recoils from pain as the Chief Evil, and so far as possible avoids it. This it does as long as it remains unperverted, at the prompting of Nature's own unbiased and honest verdict.
Hence Epicurus refuses to admit any necessity for argument or discussion to prove that pleasure is desirable and pain to be avoided. These facts, be thinks, are perceived by the senses, as that fire is hot, snow white, honey sweet, none of which things need be proved by elaborate argument: it is enough merely to draw attention to them. (For there is a difference, he holds, between formal syllogistic proof of a thing and a mere notice or reminder: the former is the method for discovering abstruse and recondite truths, the latter for indicating facts that are obvious and evident.) Strip mankind of sensation, and nothing remains; it follows that Nature herself is the judge of that which is in accordance with or contrary to nature. What does Nature perceive or what does she judge of, beside pleasure and pain, to guide her actions of desire and of avoidance?"
So in this kind of chain of reasoning the Epicureans first start off and ask: "We are inquiring, then, what is the final and ultimate Good, which as all philosophers are agreed must be of such a nature as to be the End to which all other things are means, while it is not itself a means to anything else." They give the answer "pleasure" (which is a feeling) and as proof they say "that is what all animals do at birth before there is any possibility of corruption." They also point out as a second proof that absent feeling of some kind, the organism is dead. And they point out that we know these things by feeling alone -- in the same way we know that sugar is sweet, so there is no possibility of mistaken opinion corrupting our conclusion. (Thus "logic" is deprecated as subsidiary to the canonical faculties - 5 senses, anticipations, and feeling - which operate automatically and without opinion.)
Be sure to note here that in this "canon of truth," "truth" is not something give by god or as an ideal form -- all truth is something that is "true to us" or "true to a normal human being in those same circumstances." "Truth" is not something that floats in the air (Platonic ideal forms) or given by god (religious revelation) or existing as "essences" within the things around us (Aristotle). None of those alternative means of knowledge are true, according to Epicurus. The only "truth" is that which is real to us through our sensations/anticipations/feelings.
As to "hedonism" there is no accepted "author" or authority who can answer such questions or tell us what the "right answer according to Utilitarianism" is. Of course i might be fair to say that "Utilitarianism is what Jeremy Bentham said it is" but I doubt that you mean it that way; you are thinking there is an accepted definition and I don't think there is.
Now maybe Bentham defined "the greatest good of the greatest number" as the ultimate good of Utlitarianism. If so, we would need to look to see exactly how he stated that, but even if he said that, he's not advanced the ball at all because he has not defined "good." If we are asking "what is the ultimate good?" then to answer "the greatest good of the greatest number" is circular or even nonsensical. I am pretty sure that Bentham has not said "good = pleasure" but I am not an expert on Bentham or how he might have defined "good."
That's the kind of analysis Daniel that I am suggesting needs to be made. You'll find that Epicurus had a very clear set of principles which you can outline, and based on the answers you can line up basic positions on "What am I? (physics)" "What is the good?"(ethics) and "How do I know it with confidence?"(epistemology / canonics). You can basically do that with Plato, Aristotle, and the Stoics as well, but the answers are much different.