Pete, I can't contribute too much except for the weather question (from a state and a half over). I'd look at early fall, say leaving in September, and think about going north to south. In the spring, you've got a good chance of rain 1/3 to 1/2 of your days, and occasional Really Bad Weather. Of course, since we had that this year, next year may be lovely.

If you can make it in a month, March is usually the worst fire month (meaning driest weather, leaves, and trees) in the southeast, so you might want to start then. TVA plans to start filling its upstream reservoirs April 15, and they usually really start 2-4 weeks early when the spring storms hit. Again, the floods were bad this year, so next year may be dry with low rivers all along your route.

South to north would be better in the spring, as you follow thawing temperatures north. Reverse is true for the fall, as you race cold weather south. Mid-September to October is usually the best cycling weather for northern Alabama and Tennessee.