Even the father of the cotton gin claims that neccessity is the mother of invention. Furthermore, many of the inventions that pushed the Industrial Revolution were invented by common people without a college education.
Ask any farmer which would they rather have, a combine or 1,000 slaves...they'd much rather have the combine. A combine is far cheaper in the long run to maintain and is more effecient. The South's reliance on slave labor is part of the reason they lost the Civil War. They simply were not as productive.
You argument that inventions of the industrial revolution only holds water if you can prove a causal relationship between the ownership of slaves and the propensity of one to invent. You can't because there is a statistically significant (hell even a a p-value of .10) relationship between the two.
As for the college comment, explain how the "best" colleges are located in states that held slaves for the briefest period of time.
For example:
School , State , Years allowed slavery before development of institution
Penn PA 101
Harvard MA 7
Dartmouth NH 124
Yale CT 62
Brown RI 112
Cornell/Columbia NY 239/128
Princeton NJ 119
See, the numbers are all over the place. And if you want to count early southen states such as North Carolina (Wake Forest), Tennessee (Vanderbilt), and Floria (Miami) you argument looks even worse.
I think you have been doing too much listening to philosophy and not enough math to back it up.