I tested as "Midland", too. I was born in Germany, raised in Kansas by a German mother and a father from Nebraska. I have lived most of my adult life in Southeast Texas. Of course I don't have an accent!
One time a friend from my hometown (Leavenworth) came to see me after many years, and she claimed I had developed a Southern drawl. I'm sure all the native Texans around me would have laughed at that. However, when I go back to Kansas now I do notice a few words that sound a little wrong to me. Can't quite pinpoint what's different.
The most interesting thing I've read on the subject of regional dialects in this country was a statement that at the time of the Civil War, there was no southern accent, or it was, at least, very different from what developed by the time we arrived. I wish I could remember where I read that. I would like to see some documentation. Surely speech couldn't evolve that drastically is such a short time. On the other hand, I think the whole country now sounds more like Southern California than it did when I was a kid, just because of the influence of TV and movies.