Wes,
I think you'll find the classic LSA route is "follow I-20 east, and work your way down to I-10 somewhere before Tallahassee". Lot of options along 20.
Across south Alabama, Monroeville, Evergreen, Greenville, or Bainbridge GA are good stops.
When you get just past Tallahassee, the best route is to shadow Florida Hwy 19 south across the swamps to someplace near Crystal River. Hwy 19 is much like a giant white concrete airstrip; legend says they built it that way on purpose, but who knows? Plant City or Cross City are traditional stops, and there's a Dairy Queen next to the FBO at Crystal River. From CR head for the NE corner of the Tampa Class B and then on to Lakeland.