This "Vatican Saying" doesn't get referenced a lot. In fact, before working through the list, I don't know if I ever came across it!
Saint-Andre doesn't include it in his list as it's obviously NOT a saying of Epicurus. Here is Bailey's transcription, translation, and commentary:
We're familiar with αυταρκειας (autarkeias "self-sufficiency" or "self-reliance"), but ημεροτητος (hemerotetos) is "gentleness, kindness (of the greatest kind)."
Bailey's comment "Epicurus fully satisfied the Stoic standard" encapsulates some of the issues with Bailey's overall approach to his interpretation of Epicurean texts. He seems to often filter them through a Stoic or ascetic lens.
Autarkeia αὐταρκείας comes up in Epicurean texts, most likely predating and separate from Stoic texts. I don't think Stoics were as much of a rival in the early days of Epicurus's school as they would become later.
VS44. When the sage contends with necessity, he is skilled at giving rather than taking — such a treasury of self-reliance has he found.
ὁ σοφὸς εἰς τὰ ἀναγκαῖα συγκριθεῖς μᾶλλον ἐπίσταται μεταδιδόναι ἢ μεταλαμβάνειν· τηλικοῦτον αὐταρκείας εὗρε θησαυρόν.
VS45. The study of what is natural produces not braggarts nor windbags nor those who show off the culture that most people fight about, but those who are fearless and self-reliant and who value their own good qualities rather than the good things that have come to them from external circumstances.
οὐ κομποὺς οὐδὲ φωνῆς ἐργαστικοὺς οὐδὲ τὴν περιμάχητον παρὰ τοῖς πολλοῖς παιδείαν ἐνδεικνυμένους φυσιολογία παρασκευάζει, ἀλλὰ σοβαροὺς καὶ αὐτάρκεις καὶ ἐπὶ τοῖς ἰδίοις ἀγαθοῖς, οὐκ ἐπὶ τοῖς τῶν πραγμάτων μέγα φρονοῦντες.
VS77. The greatest fruit of self-reliance is freedom.
τῆς αὐταρκείας καρπὸς μέγιστος ἐλευθερία.
Fragment 135a. We value self-reliance not so that we will live simply and cheaply in all things, but so that we will not be consumed by them.
ἐζηλώσαμεν τὴν αὐτάρκειαν οὐχ ὅπως τοῖς εὐτελέσι καὶ λιτοῖς παντῶς χρώμεθα, ἀλλʼ ὅπως θαρρῶμεν πρὸς αὐτά.
Fragment 200. Don't think it unnatural that when the body cries out, the soul cries also. The body says don't be hungry, don't be thirsty, don't be cold. It is difficult for the soul to prevent these cries, and dangerous for it to ignore the commands of nature because of attachment to its usual independence.
ἀφυσιολόγητον μηδὲν ἡγοῦ βοώσης τῆς σαρκὸς βοᾶν τὴν ψυχὴν· σαρκὸς δὲ φωνή· μὴ πεινῆν, μὴ διψῆν, μὴ ῥιγοῦν· καὶ ταῦτα τὴν ψυχὴν χαλεπὸν μὲν κωλῦσαι, ἐπισφαλὲς δὲ παρακοῦσαι τῆς παραγγειλάσης φύσεως αὐτῇ τῆς προσφυοῦς αὑτῇ αὐταρκείας καθʼ ἡμέραν.
Fr. 202. He who follows nature and not groundless opinions is completely self-reliant. With regard to what is enough by nature, everything he owns is a source of wealth; whereas with regard to unlimited desires, even the greatest wealth is poverty.
ὁ οὖν τῇ φύσει παρακολουθῶν καὶ μὴ ταῖς κεναῖς δόξαις ἐν πᾶσιν αὐτάρκης· πρὸς γὰρ τὸ τῇ φύσει ἀρκοῦν πᾶσα κτῆσίς ἐστι πλοῦτος, πρὸς δὲ τὰς ἀορίστους ὀρέξεις καὶ ὁ μέγιστος πλοῦτός ἐστι πενία.
Fr. 476. Self-reliance is the greatest wealth of all.
πλουσιώτατον αὐτάρκεια πάντων.