TZ missed naming the Cotton States Special, which split off from the Southern States Special in Hamlet, and headed for Birmingham. This was eventually displaced by the Silver Comet,
I don't know just what span of years the trains were operated, but towards the end of the thirties SAL had the overnight Birmingham Owl and Atlanta Owl, which ran between Atlanta and Birmingham.
I rather doubt that this was properly heavyweight when it was inaugurated, but a 1910 SAL TT shows the Flamingo (yes, SAL had one, too) between New York and Florida points. Of course, Amtrak has not yet operated a one-legged bird.
In 1941, I rode the New York-Florida Limited and the Robert E. Lee. My mother, my oldest brother, my youngest brother, and I boarded in Camden to go up to Virginia to visit relatives. Since we were being met in McKenney, where the New York-Florida Limited did not stop, we detrained in Raleigh and waited for the Robert E. Lee, which did stop at McKenney, on flag. And, except for my oldest brother, who was in college, we were riding a pass. Going back home, we boarded the New York-Florida Limited in Petersburg becasue it did not stop in McKenney-- and the conductor did not ask for any fare even though the pass read from McKenney to Camden. The day after we got back home, I started to school.
Johnny