Having made this trip several times. I would head south on I-75 to Cincinnati, OH. Then I-71 toward Louisville, KY. I-65 to Nashville, TN. The I-65 to Birmingham, AL. Then head West on I-20 to I-10.
I have a APP on my I phone called Trip Weather. Put your trip into it with you leaving Sunday. Most of the trip especially in OHIO is RED. Meaning bad weather conditions for driving. When leaving the Detroit area I always monitor weather to determine when to travel what route to take.
You should be able to dewinterize by the time you get to Nashville.