In my view, the war could have been done better had the CS attempted its best to reframe the war as a war against the encroaching monied and corporate interest of Northern Industrial capital. During the war and immediately after, the most serious anti-Union or otherwise uniquely southern mentalities that took shape in politics were framed around a sort of Jeffersonian Southern socialism. The reason such an ideology and reframing would be efficient if performed well enough, is that it could have possibly had the effect of lowering Northern participation and possibly been able to take advantage of disunity in the Northern states.
In general, I am surprised considering the results of history in other lands in otl, that this did not happen otl after the CS lost. That is, dissatisfaction was extremely high in the poor communities of the South, who sought to overturn the order set forth by the US victory, not for the restoration of slavery of aristocratic economy, but more as a statement of revenge and against the general perceived trends of capitalist intrusion into the previously less economically involved rural poor across the South. This would have happened in otl if the rise if the Lost Cause mythos and the Bourbon-Redeemer styled Democrat did not occur or arise. If the former Southern elites and the middle class had went alongside the rural poor in a narrative of vengeance, instead of Lost Cause, the situation of the Union would be much different than otl.
Indeed, as
@Skallagrim has discussed elsewhere, the Southern states possessed as its primary reason for secession, the notion that the South, for whom they held the US was founded for, was losing its grip on power in the US. The growth of Northern industrial cities through immigration and the expanding prowess of a nascent corporate interest frightened the Southern elites, who had for many decades prior dominated or at least held preeminence over the US institutions, especially the electoral college and the production of presidents. If we understand that the reasoning for their separatism was this fear of losing control and power, if the Southern leadership, especially the Fire-Eaters and so forth, can flip the reasoning into more broadly, an anti-urban and anti-capitalist (in the sense of the growing power of the major corporate entities) movement and revolution seeking to break the back of the US' infiltrating leadership, one may see that their ability to cause disunity in the US raise exponentially and likewise possibly expand its borders.
Generally, if the South wishes to succeed, in my view, the best way to do so is to find some way to break the US to pieces and this is the only way that I can imagine without enormous foreign assistance (which may not be enough) or the CS gains victories that would become legendary. Once the US is broken and defeated, the CS can then freely separate and live its southern visions, yet by opening the door on socialist styled rhetoric, the matter may become such that the CS leadership will lose authority in its own lands, as a tide of revolution sweeps across the US in a fervor of both unification and in wealth redistribution by the year 1910.