Okay, since I couldn't find anything in DeWitt or in Clay to satisfy me, I went through and picked out ALL of the uses of the word στοιχεῖον (as in Δώδεκα στοιχείωσις) and its variations within Diogenes Laertius, Book X. It's used 5 times within the letter to Herodotus (the most within Book X). I've included both the Greek and English (Hicks) from the Perseus Project below for everyone's inspection. Unfortunately, I have not had time (nor do I plan to take the time!) to go and search within Philodemus or the extant On Nature fragments. Sorry. Life is too short 
(30) Canonic forms the introduction to the system and is contained in a single work entitled The Canon. The physical part includes the entire theory of Nature : it is contained in the thirty-seven books Of Nature and, **in a summary form, in the letters.** (**καὶ ταῖς ἐπιστολαῖς κατὰ στοιχεῖον**)
The usual arrangement, however, is to conjoin canonic with physics, and the former they call the science which deals with **the standard and the first principle, or ***the elementary part*** of philosophy (περὶ κριτηρίου (kriteriou) καὶ ἀρχῆς (arkhes), καὶ ***στοιχειωτικόν (stoikheiotikon)***), while physics proper, they say, deals with becoming and perishing and with nature.
(34) They affirm that there are two states of feeling, pleasure and pain, which arise in every animate being, and that the one is favourable and the other hostile to that being, and by their means choice and avoidance are determined; and that there are two kinds of inquiry, the one concerned with things, the other with nothing but words.So much, then, for his division and **criterion in their main outline**. (καὶ τοῦ κριτηρίου στοιχειωδῶς.)
From the Letter to Herodotus:
(35) Those who have made some advance in the survey of the entire system ought to fix in their minds **under the principal headings an *elementary outline* of the whole treatment of the subject** (ἐν τῇ τῶν ὅλων ἐπιβλέψει τὸν τύπον τῆς ὅλης πραγματείας τὸν *κατεστοιχειωμένον*). For a comprehensive view is often required, the details but seldom.
(36) ...since it is the privilege of the mature student to make a ready use of his conceptions by referring every one of them to ***elementary facts and simple terms** (πρὸς ἁπλᾶ στοιχειώματα καὶ φωνὰς (apla phonas "simple terms")).
(37) Hence, since such a course is of service to all who take up natural science, I, who devote to the subject my continuous energy and reap the calm enjoyment of a life like this, have prepared for you just such **an epitome *and manual* of the doctrines as a whole** (τινὰ ἐπιτομὴν (epitome) *καὶ στοιχείωσιν* τῶν ὅλων δοξῶν).
(44) But that colour varies with the arrangement of the atoms he states in his "Twelve Rudiments" (τὸ δὲ χρῶμα παρὰ τὴν θέσιν τῶν ἀτόμων ἀλλάττεσθαι ἐν ταῖς Δώδεκα στοιχειώσεσί φησι.)
(47) For if it changed its direction, that would be equivalent to its meeting with resistance, even if up to that point we allow nothing to impede the rate of its flight. **This is an *elementary fact* which in itself is well worth bearing in mind.** (χρήσιμον δὴ καὶ τοῦτο κατασχεῖν *τὸ στοιχεῖον*.) (NOTE: This is the one mention that gets close to stating this is one of the elements: Something like "Atoms don't change their direction or speed"??)
From Letter to Pythocles:
(86) We do not seek to wrest by force what is impossible, nor to understand all matters equally well, nor make our treatment always as clear as when we discuss human life or explain the principles of physics in general--for instance, that the whole of being consists of bodies and intangible nature, or **that *the ultimate elements of things* are indivisible** (ὅτι ἄτομα *<τὰ> στοιχεῖα*), or any other proposition which admits only one explanation of the phenomena to be possible.
From Letter to Menoikeus:
(123) Those things which without ceasing I have declared unto thee, those do, and exercise thyself therein, holding them to be ** *the elements* of right life**.(στοιχεῖα τοῦ καλῶς ζῆν)
Clay says "His (Epicurus's) language makes it plain that he regarded the nine propositions set out earlier in the letter as stoicheia... "kai de touto" looks back to the stoicheiomata and their usefulness." I'm still unclear on how Clay is slicing the Letter to Herodotus to come up with only nine stoicheiomata, and the number is clearly 12 "elements." So, why would Epicurus only include 9?
I *think* I'm willing to accept that the Δώδεκα στοιχείωσις *probably* referred to the physics of Epicurus, BUT in Section 30, Diogenes Laertius specifically talks about Canonic being the στοιχεῖον... So, again, as I did earlier, I ask: Did the Twelve Elements refer to the atoms, void, physics stuff or did it refer back to the use of the senses within the canonic? Both DeWitt and Clay seem too self-assured for my full endorsement of their lists.
And I see what Clay was trying to do, I think, in calling the article after Epicurus's will. He's trying to say that even though Hermarchus is his philosophical heir, it is actually Lucretius who ends up being his "heir" because we get Lucretius's whole poem to carry on Epicurus's philosophy. Yeah, that's a little arcane.
Thoughts welcome!!
Well, okay... As long as you don't have any strong feelings....