You need to check about traveling on I-10 as you go east to avoid confrontation with the law. Bicycles are not allowed on interstate highways in the eastern states. It is allowed in the west because there is often no other option. I would only "wing it" if you have good local advice on routes and you are planning to shorten the route. If you shorten the route by cutting across GA further north than the Southern tier route stay south of the fall line (Columbus, Macon, Augusta). You will stay in the relatively flat coastal plain and avoid the hilly piedmont. This would hold true for SC and NC as well.

You are doing amazingly well on your schedule and tour. May the wind be at your back!