Here is where I've done winter tours before:
1. In San Diego, I did the Christmas ride four different times. Good route and ~400 mile loop.
2. I did my own ride in Texas. I rented a car one-way to drive to Brownsville. Over the ensuing week I cycled to Dallas.
3. I've done organized rides in Florida. The coasts are busy and hectic, but the interior is pretty reasonable and quieter spots.

I've done the Natchez Trace in late October, but suspect the nights particularly on northern bits will be just a bit colder than you look for above. If you got yourself to San Antonio, I could see putting together a loop around to Del Rio and back. Similarly, I'd look for cities you could cycle between in southern US (e.g. start from place like Atlanta, GA and go roughly your distance and you'll be in Jackson, MS). Alternately, look up an organized ride like BRAG and see what cities they stopped in and plan a route along some of the same places.