Here is an ugly detour that completely avoids Atlanta. Your criteria about mileage, however, says this probably isn't so good.
Ocala, FL - Take I-75 N through/past Gainesville, FL to Macon GA.
Macon, GA - Take US 80 W through Columbus, GA through Tuskegee, AL to Shorter, AL
Shorter, AL - Take I-85 W to Montgomery, AL
ALTERNATE POSSIBILITY: From Macon, GA - US 80 W to Columbus, take US 280 W to Opelika, GA take I-85 W to Montgomery, AL
Montgomery, AL - Take I-65 N to Birmingham, AL
Birmingham, AL - Take I-59 N to Chattanooga, TN
THE ABOVE IS A WIDE, SWEEPING DETOUR that avoids Atlanta. It goes WAY out of the way, probably more than 150 miles, but is the best route I can see to stay on good, well-traveled roads and yet avoid that sprawl of a city. I have no idea how to do this in only 100 miles of detour. May I ask why you are preparing for your coronary if you go through Atlanta?
The most direct route is I-75 N to Atlanta, then use I-285 which is the "ring road" around the city, then continue on I-75 N.