I don’t know enough about the South’s mid-19th century urban demographics to choose any candidate cities on this question, but I’ll just make the observation that there are two basic options that are open to a country (or state or province) in regard to its capital. The first option is for the capital (the centre of political power) to be the same city as the metropolis (the largest city, and typically the centre of economic power). In France, Paris plays both roles; ditto in Britain for London. The second option is for these two cities to be separate. This is the case for the US and Canada, in which Washington and Ottawa are the capitals and New York and Toronto are the metropolises.
As regards the Confederacy, I guess I’d argue that it’s more important for a warring country to defend its prime economic and industrial centre than its political capital. Political centres (say, from Paris to Vichy) can be moved much more easily than industrial ones (as the Russians had to do in 1941). This portability can be illustrated by the answer than an official (I can’t recall who) of the newly formed Confederate government once gave to a visitor who asked him where he could find the State Department. “Under my hat,” he said, “and the archives in my coat pocket.”