My Mom is from Kentuky, and since she taught me how to talk, I've had a lot of people ask me if I used to live in the south myself. A friend of mine said she used to think that because sometimes I would "talk slow." After I got over the initial insult, she explained that I would draw out my vowels and always seemed tired.
You might also try to find Coal Miner's Daughter to rent. They used actual locals in many of those scenes, so it's authentic. Find youtube videos of interviews with Kelly Pickler and Carrie Underwood too.
I think Julie's advice that she doesn't have to have a strong accent is very sound. My guess is right now they're just trying to see who has the ability to pick up the accent properly.