http://news.nationalgeographic.com/news/2003/01/0131_030203_jubilee2_2.html
All your examples concerning cotton relate to an era several decades after the 1790s. During the 1790s, tobacco was the main southern crop in Virginia and NC and cotton was grown mostly in SC and Georgia. And the territories that became the other southern states hadn't even been opened for very much settlement.
At the time the Constitution was written, the economy of the southern states was totally reliant on slave labor.
The remark relates to the 1790s, not 1850. Much of central Alabama was still inhabited by the Creek Indians until their defeat by Andrew Jackson in 1814. The cotton growing south didn't exist in 1790.
The link above went dead for some reason.
http://news.nationalgeographic.com/news/2003/01/0131_030203_jubilee2_2.html
Buy that?
At the time, I believe the most important single crop in the south was indigo -- concentrated in South Carolina and grown in the hot, humid coastal plain.
Very labor intensive -- moreso even than cotton.
Frankly, I don't know why we're still quibbling on this topic. On the one hand, it seems obvious that "totally" was an overstatement and thus inaccurate. And, by the same token, it seems obvious that -- even in the 1790's -- the economy of the south (defined as Virginia thru Georgia) was largely (mainly, importantly, strongly) reliant on slave labor.
Indeed, the best proof of that claim may be that the southern states were prepared to depart the Confederation over it. And they were doubtless the best judges of just how reliant their economy was on that "peculiar institution" at the time.