Actually, Calhoun's economic beliefs largely surrounded the tariff issue, which he took on from an increasingly free-trade view as his career progressed. If any American political player of the time espoused the Labor Theory of Value, it was Abraham Lincoln, not Calhoun.
Lincoln did this across decades of his career and asserted the theory repeatedly. It's most specific consideration is found in the notes from a speech he gave on tariffs in the late 1840's, but the idea emerges and is referenced by Lincoln again and again in the 1850's and as president.
and George Fitzhugh, which neo-Confederates have scrupulously avoided
Fitzhugh is avoided today much for the same reason that he was avoided in his own day. He was a crackpot fringer. His ideas are certainly disturbing, bizarre, and socialist-minded but, as any good historian will tell you, on the fringe in his own day, not to mention today.
It was not only the cause of the war, it was THE ONLY reason for the formation of the modern Democratic Party, and that is what is even more amusing about neo-Confeds. To attack Lincoln, they have to link arms with the Democratic Socialists. HAHAHAHAH.