Mike, I traveled from San Diego to Jacksonville, then north to Philly a couple of years ago. Most of the ride across country was done with the Southern Tier maps, although I did stray off the route a few times with varying success. I spent more time on US 90 than Adventure Cycling recommends. It only really hurt me in Louisiana. I would say, stick to the approved route in that state.
From Jacksonville north I spent a lot of time on US 17, then I hugged the coastline. You might want to check out the Donna Ikenberry book "Bicycling the Atlantic Coast" before you decide how you want to travel south.
Although I've never done this ride, you could also consider traveling south on the Blue Ridge Parkway, Skyline Drive, and Natchez Trace Parkway. I'm not sure how to get from the Skyline to the Trace, but it might be possible. And, you're close to the starting point of the Blue Ridge.
Good luck, and have fun.