Excellent question, Matteng!
Regarding the fourth criterion of the canon, I will simply point the way to Prof. David Glidden's Epicurean Prolepsis. It won't furnish any answers, but in it he does attempt to explain why the question itself is extremely confusing, and why we should tread carefully.
Regarding the passage you have quoted from Hiram's essay, we have direct evidence of this method in the Letter to Pythocles:
Quote[95] for in our own experience we see many things which shine by their own light and many also which shine by borrowed light. And none of the celestial phenomena stand in the way, if only we always keep in mind the method of plural explanation and the several consistent assumptions and causes, instead of dwelling on what is inconsistent and giving it a false importance so as always to fall back in one way or another upon the single explanation. The appearance of the face in the moon may equally well arise from interchange of parts, or from interposition of something, or in any other of the ways which might be seen to accord with the facts.
[95] καὶ γὰρ παρ᾽ ἡμῖν θεωρεῖται πολλὰ μὲν ἐξ ἑαυτῶν ἔχοντα, πολλὰ δὲ ἀφ᾽ ἑτέρων. καὶ οὐθὲν ἐμποδοστατεῖ τῶν ἐν τοῖς μετεώροις φαινομένων, ἐάν τις τοῦ πλεοναχοῦ τρόπου ἀεὶ μνήμην ἔχῃ καὶ τὰς ἀκολούθους αὐτοῖς ὑποθέσεις ἅμα καὶ αἰτίας συνθεωρῇ καὶ μὴ ἀναβλέπων εἰς τὰ ἀνακόλουθα ταῦτ᾽ ὀγκοῖ ματαίως καὶ καταρρέπῃ ἄλλοτε ἄλλως ἐπὶ τὸν μοναχὸν τρόπον. ἡ δὲ ἔμφασις τοῦ προσώπου ἐν αὐτῇ δύναται μὲν γίνεσθαι καὶ κατὰ παραλλαγὴν μερῶν καὶ κατ᾽ ἐπιπροσθέτησιν, καὶ ὅσοι ποτ᾽ ἂν τρόποι θεωροῖντο τὸ σύμφωνον τοῖς φαινομένοις κεκτημένοι.
The word translated as method in this passage is τρόπος, trope, or way. The way of manifold explanation; when confronted with a strange new phenomenon (φαινομένων), one should begin be considering the various natural hypotheses (ὑποθέσεις) or potential causes (αἰτίας) that might possibly have given rise to the phenomenon. These potential explanations must harmonize with sense perception, and also with known facts. All of this is in contrast to the way of the single explanation, which constitutes an arbitrary selection of one possible explanation to the exclusion of all others.
It's important to remember that the purpose of this exercise is not to develop a robust or rigorous scientific explanation for every phenomenon. The purpose is to eradicate fear. For example; are bolts of lightning hurled down by Zeus in order to punish hubris, as in the myth of Phaeton? There is no reason to think so; that is just one possible explanation, and that particular explanation isn't even a good one. As Lucretius notes (book 2, line ~1100), thunderbolts are often seen to strike the temples of Olympian Zeus himself. The explanation, in other words, does not accord with known facts.