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Here are current/prior "Paddle Georgia" maps; http://www.garivers.org/paddle_georgia/maps.html. For the "brave" folks, here's a list of GA whitewater opportunities; http://www.riverfacts.com/states/ga.html.
The Chestatee River.
Whitewater Paddling Rivers in Georgia including the easy Cartecay River.
South Carolina
- Congaree National Park; https://www.nps.gov/cong/planyourvisit/trip-ideas.htm
Alabama
- Bartram Canoe Trail (200 miles); https://www.canoekayak.com/canoe/destination-alabamas-bartram-canoe-trail-offers-year-round-paddling/?wc_mid=4036:10740&wc_rid=4036:2817941&_wcsid=68C1EE4FB9FF5683CA16AA24113EDBC947717666958DDB18
Long Distance Paddling (aka Pipe Dreams)
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As the wikipedia article states, the Trinity River is 710 miles long stretching from just under the Red River (i.e. Oklahoma) down to the Trinity Bay which is part of Galveston Bay (i.e. the Gulf of Mexico). I'd imagine starting right at the tip of the official Trinity River in NW Dallas and taking it all the way down to the bays. These fellas had a short little adventure near the top of my suggested route; http://dallastrinitytrails.blogspot.com/2012/11/exploring-trinity-river-by-canoe.html.
Northern Forest Canoe Trail
Article at https://www.canoekayak.com/canoe/solo-on-the-northern-forest-canoe-trail/?wc_mid=4036:12093&wc_rid=4036:2817941&_wcsid=68C1EE4FB9FF5683CA16AA24113EDBC929845CC882D9C1DA documenting a solo attempt on the 740 mile Northern Forest Canoe Trail.