Call Drexler up in Chicago. They used to take my horse from Chicago to the TN/VA border when I was in school. I think the subcontracted the second part of the trip to Carolina Horse Transport, but this was many years ago.
C&E or Tony Aprile would be my best guesses. They run (or used to) the I-65 corridor from Chicago to Florida and back. I thought Drexler did, too. I used Tony Aprile (708-903-7574) to ship a horse a few years back from FL to KY- I have nothing but good to say about the experience. Definitely A+ service!