I can't say I know much about the differences between New England ghost stories and Southern ghost stories. It sounds like that podcast is taking a very particular snap shot (after all, "industrial accidents" and "immigrants" wouldn't appear until the 19th century). One very distinctive difference between the South and the North, however, that long predates the 19th century is the large presence of African Americans in the South. Of course, there were African Americans in the North from the very beginning, as well--let's not forget that the start of the Salem Witch Trials seems to be, in part, Tituba (who many believe to be fully or partially of African descent, though others argues that she was purely indigenous) telling "ghost stories" to young women and these at least some of these "nice little Puritan girls" feeling tremendous guilt about these scandalous, possibly "Satanic" stories--so even here the difference may be in degree rather than an absolute one. Still, there is a much stronger presence of African-Americans, and therefore distinctly African American customs, in the South. Again, I don't know the particularly variety of stories you're covering, but many of the Southern traditions that I know are strongly influenced by African-American (and African) customs. Not just the famous Br'er Rabbit, et al., but also ideas about rootwork, haints, and hoodoo (obviously a cognate of Haitian Voudon and the Lousiana Voodoo). /u/splattingwallendas asked about the distinct influence of French and Spanish ghost stories in Louisiana and Florida, but when I think of the distinctness of Louisiana folk customs, I tend to think of the heavier influence of primarily African-American traditions (like Voodoo, which of course also incorporates some French, Catholic, and Native American ideas) more than I think of distinctly French or Spanish ideas (other than the Catholic influence, of course). This isn't my area of speciality, but, assuming i) that there are differences in Southern and Northern ghost stories and ii) these differences are not primarily due to 19th century differences in ecology, I would be surprised if the origin of these differences lie primarily in Europe.

One additional source of differentiation might the different influences of spiritualism. As discussed, these seem to be mainly 19th century stories, and one of the big, big spiritual/religious movements of the 19th century that we often forget is "spiritualism". The crystal balls and seances and Allan Kardec all of that stuff. I would guess that this had more of an influence in the North than the South, just because all of the stories I've heard of 19th and early 20th century spiritism in America come from Northeastern and Midwestern cities. Spiritism/Spiritualism, though we normally see it as a hokey movement now, was hugely influential and many, many very smart, very respectable people took it quite seriously. One of the big differences in the Candomblé and Umbanda, the two big vernacular religious traditions of Africa-American origins in Brazil, is the degree to which they have incorporated spiritist beliefs (Umbanda I believe has more, and I believe there are also still groups in Brazil that have much more straight-line Kardecian influences--see for example Chico Xavier).

So, again, not knowing the stories you're talking about but knowing the general vernacular "spiritual environments" of the areas, I would expect a greater Spiritist influence in New England ghost stories and a great influence from the African-American vernacular tradition in Southern ghost stories.

As a side-note to what OP said does anyone have any readings on ghost stories from ancient times such as Ancient Rome, Greece, or Mesopotamia? I feel like many would be rather similar to modern stories. (Not sure if this is too far off topic)