Let me go at this a diffrent way. Can we get a Southern Republican, not necessarily an officeholder in OTL, in a high office, like Secretary of Treasury or such, and parley that into a run for the Presidency later on? I ask because it seems to me like there is very little suggestions for any real candidates, which probably mimics the enthusiasm most of those men faced nationwide.
James Longstreet, after the Civil War, actually became a Republican and served as both a state official (adjutant-general for the Louisiana militia) and federal appointee (having been the ambassador to the Ottoman Empire under Garfield and Commissioner of Railroads under McKinley/Teddy Roosevelt). He was also, supposedly, briefly considered by Rutherford B. Hayes to be Secretary of the Navy. Remove the blemish of the Battle of Liberty Palace, in which he and his Reconstruction-loyalist militia were routed by an anti-Reconstruction mob, and he might've soared even higher.
Of course, the idea of a successful Confederate general becoming President of the United States is...well, it's something that ought to have a TL done about, because there's enough fodder there OTL to kludge together something with a thin veneer of plausibility re: Longstreet.