I'll go further out on a limb and posit that EP is the study of nature (Epicurus advised the study of nature though I don't know that he went so far as to say his philosophy is the study of nature), then you arrive at pleasure as the goal through intense examination of pleasure and pain and how they occur in the body and mind. This is perhaps how you come to an understanding of intensity, location and duration (ILD for short).
Labeling mental and physical pleasures may come either before or after in this process, but a detailed understanding comes from understanding ILD.
Having a format (such as Lucretius) that explicitly introduces the philosophy as the study of nature, and from there gets to pleasure as the goal might be a useful modern pedagogy.