Just as additional info, as this doesn't answer your question (sorry!):

I've seen constructions like this popping up in other languages, under different names. In Portuguese for example it's called "pronome de interesse" (pronoun of interest) or "dativo ético" (ethical dative). Often used alongside commands, like this:

• Por favor, não [me]¹ conte [para os outros]² [o que aconteceu]³.
• Please, [for my sake]¹, don't tell [the others]² [what happened]³.

I've tagged 1 = the ethic dative, 2 = the indirect object, and 3 = the direct object. Since the verb (contar, to tell) already got its two objects, that ⟨me⟩ cannot be an object requirement of the verb.

It's typically associated with informal speech, but attested across multiple dialects (see e.g. this and this). And apparently it backtracks all the way into Latin.

German and Ancient Greek also show the same phenomenon.

Based on that I'd probably guess that what you're seeing in English is the leftover of some really old feature, so it'll probably surface across multiple dialects, even if Dixie English sticks with it a bit more.