Steve Reece was kind enough to reply to my email and directed me to academia.edu, where I was able to download his article.
The second half of the expression, βραδεῖς τῇ καρδίᾳ ‘slow in heart’, occurs nowhere else in Jewish or Christian literature. In fact, in the entire Septuagint and New Testament the adjective βραδύς occurs only here and in Jas 1.19, in an equally aphoristic expression, again with Classical rather than Septuagintal or New Testament resonance: ἔστω δὲ πᾶς ἄνθρωπος ταχὺς εἰς τὸ ἀκοῦσαι, βραδὺς εἰς τὸ λαλῆσαι, βραδὺς εἰς ὀργήν ‘let every man be swift to listen, slow to speak, slow to anger’. From Classical and Hellenistic literature, on the other hand, one can compare such similar expressions as προνοῆσαι βραδεῖς ‘slow to understand’ (Thucydides 3.38.6) and βραδὺς πρὸς ὀργὴν ‘slow to anger’ (Menander’s Sententiae 60). In short, the expression ὦ ἀνόητε/ἀνόητοι καὶ βραδὺς/βραδὺ/βραδεῖς τῇ καρδίᾳ is lexically and syntactically more Classical than Koine, and it resides more comfortably in a pagan context, such as in Aesop’s fables, than in a Jewish or Christian context, such as in the gospel of Luke.
I don’t think that he’s correct about this. The “βραδεῖς τῇ καρδίᾳ” is a very stark Septuagintism, and doesn’t really have classical parallels.
καὶ Ροβοαμ ἦν νεώτερος καὶ δειλὸς τῇ καρδίᾳ
καὶ πᾶς πρόθυμος τῇ καρδίᾳ ὁλοκαυτώσεις
καὶ συνῆλθον αὐτῷ πάντες οἱ εὔψυχοι τῇ καρδίᾳ
I could continue. In the NT, famously:
πραΰς εἰμι καὶ ταπεινὸς τῇ καρδίᾳ
Perseus doesn’t include Septuagint uses, but it’s worth searching for the string “τῇ καρδίᾳ” or even “καρδίᾳ” and noting that the use is mainly NT Greek.
And his point about βραδύς is a bit overstated, in my opinion. The adjective is rare, but there are forms like: βραδύγλωσσος, various uses of βραδυνῶ, βραδέως, βραδυπλοοῦντες, βραδυτής.