Now that GA and SC have GOP legislatures is it likely that AL, LA and MS will follow suit any time soon?
That would depend on how liberal and unpopular among conservative and moderately conservative southern voters the (visible) head and symbol of the Democratic Party is. And there is always the possibility that many of those Democrats who control the legislatures in the states you have mentioned could switch to the Republican Party as their counterparts did in Georgia. It wouldn't require any effort by the state GOP to oust entrenched Democratic incumbents if those same incumbents decide that is in their best interest to run as Republicans instead of Democrats.