I think more importantly, steam mills solved for a problem the south did not have. If one was to tell a southerner, I have a technology that will save on labor costs, the southerner's response would have been "what are labor costs?"
I'd venture that the north's earlier industrialization built up experience and supporting infrastructure which made it a dubious business prospect for any southerner that might have considered building a factory, along with the fact that making textiles by manpower alone made less money than picking cotton and exporting it.
It looks like the south does have some suitable rivers, but you wonder why they exported their crops to the north just to buy them back again in their more processed form...that just doesn't make much sense from an economic standpoint. Clearly slavery wasn't a suitable replacement for the type of production work done in the north. It must have been a mix of social factors, combined with the fact that the north specialized in industry early on and you couldn't compete very well with the lack of expertise and lack of industry which supported the local industry in the south.
Anyway this is all just wild speculation. Take it for what you will.