We just bought a house in Cape Coral, but have been going back and forth to the SW Florida area from Illinois for over 30 years. If you want to avoid steep grades and Atlanta.....here is the route I would take.
I-75 north to I-10 west. Take U.S. Rt. 231 north from I-10 to Montgomery AL. At Montgomery take I-65 north to Nashville. At Nashville take I-24 to I-57. Stay on I-57 north to I-64 west to St. Louis. And of course at St. Louis get I-70 toward Kansas City and your final destination.
By using this route your only congested area will be around Nashville and St. Louis. U.S. Route 231 is almost all 4-lane divided and most of it is new pavement. You do go through some small towns and some stop lights, but we love that part of Alabama and are never in a hurry anyway.
We just ran that route pulling 16,000 pound fiver (except we went to Illinois from Cape Coral) and we will be doing it again next month pulling a 24' enclosed trailer.