Hello!
I'm interested in studying this text but so far haven't been able to find an English translation (or even a translation into another modern language). The 1916 scholarly edition by Diels (in German) is available, but while Diels provided extensive commentary, he didn't include an actual translation of the text on the columns, as fas I can tell. The author of the [wentiers blog has provided several translated extracts, from a paper by Essler, and I've read papers that cite this book by Philodemus--so it seems like a translation must exist somewhere.
It's odd that so little is available, as it seems like it could be one of our best sources available for understanding Epicurean theology, at least as interpreted by later Epicureans. It's interesting to pair it with Velleius's account in Cicero's "De Natura Deorum" as there are obvious points of alignment but also some interesting differences--vellius, for instance. asserts that the gods do not engage in any activity, whereas Philodomus denies that they are without occupation (assuming I've understood both authors correctly).