I am not finding much in the way of analysis of the Southern economy and the value created by slave labor. I was exploring this because in some states, over 50% of all households owned a slave and I wanted to see if there are numbers that tracked the economic impact of slavery in the South before they declared war.
"From this perspective, the post-War North-South disparity of roughly two-to-one in per capita income, a persistent feature of the U.S. economy between the Civil War and World War II, was basically consistent with prewar patterns."
Gavin Wright - Slavery and American Economic Development
The above has been the best I have found, but no real discussion with respect to the impact of slavery on any of those numbers. Ideally, the comparison would include the productivity of slaves against that of wage laborers in the same industry in the same state. But I realize this is a huge ask.
I'm afraid I don't have the time at the moment to write up a new answer - though I can tell you there is no agreed estimate of slavery's contribution, either in absolute or relative terms, to GDP - but you might find this answer I wrote a little while ago interesting. I think it cuts to the essence of a lot of what you're asking short of being able to give you a concrete figure for GDP (which is borderline impossible for us to achieve because GDP is not designed to account for chattel slavery), and if you have any other questions arising from what I've said there and in the other linked answers in that post, I can get around to addressing them in a couple of days time.