I think it simply comes from the bad english of italian people who immigrated to the US. Plenty of them were from South, but the stereotypical speech is simply a consequence of Italians pronouncing words as they are written (given Italian works like that).
Neapolitan dialect is actually very contracted, so the opposite of elongated vocals as the stereotype goes.
Especially if you go somewhere near Naples(the stereotypical Italian speech comes from Neapolitan, essentially)
I think it simply comes from the bad english of italian people who immigrated to the US. Plenty of them were from South, but the stereotypical speech is simply a consequence of Italians pronouncing words as they are written (given Italian works like that). Neapolitan dialect is actually very contracted, so the opposite of elongated vocals as the stereotype goes.