Not off to a good start. South Carolina doesn't make near as much sense as Alabama or Mississippi. AL or MS would have a much better chance of getting the other to join, and perhaps TN, KY, AR, LA, maybe even TX & OK, than SC would NC or GA. If this idea ever had a chance, the key to success would be strength in numbers, and putting together the largest contiguous block possible.
Of course it will never happen, but an interesting 'what if' scenario, kinda like political 'Risk' Get a solid block from TX/OK to TN/AL, and you'd then have a shot at KS & NB, which could then pull in WY and UT, maybe ID. Do all that, and GA would probably come along. Now you've got a booming, self-sufficient Southern/Flyover block, that if successful in secession would more than hold its own economically, at some point perhaps luring the Dakotas, WV, and maybe even NC and CO.
OK, back to reality.
OBTW, the new conservative republic would need a capitol, and appropriately it should go in the most miserable place possible, to insure lawmakers want to minimize their time there(and thus minimize their sessions.) So I nominate that the capitol be located either in Houston and only allowed to meet in summer, or Cheyenne and only allowed to meet in the dead of winter.
It may not happen exactly that way but think about Utah. They have their state and for the most part the Morman's view prevail there. A similar situation could happen in a southern state. I hope it does. I'd consider moving there from Massachusetts. It's getting really weird up here.
Just take everything east of the western Continental Divide, and west of the Eastern one, from Hudson's Bay to the Bay of Campeche, call it America, and let the rest of it find a new name.