my Amurrican accent

I got a box of books in the mail this week: five new Brazils, two Elinor Brent-Dyer books (Lorna at Wynyards and Stepsisters for Lorna, which I've just started), and one called The School on Castle Hillby Evelyn Simms. This one features a girl who was brought up in New Orleans, and Simms chose to write this character's dialogue phonetically. So she says things like "Avenoo", "Murcy", and "Yurrup". These startled me, because I grew up nearly 1000 miles from New Orleans, and I pronounce "Avenue", "Mercy" and "Europe" this way. In fact, I have to put on a terribly affected, very false English accent to pronouce "Mercy" differently, and I can't make "avenue" or "Europe" different at all. The only word the character and I say differently is "very", which she pronounces "vurry" (which doesn't sound like a New Orleans accent to me at all!).
So the question is: was Simms unskilled at writing phonetic versions of a Southern accent, or is my accent far more Southern than I thought?