There seems to be a two different conversations being had in tandem here. How to do away with the Lost Cause mode of historiography, which is being conflated with how to do away with the pernicious effects of racism in the South. You might be able to do away with the Lost Cause if you were to ruthlessly eliminate southern elites, people like Jefferson Davis or Jubal Early that left texts that became foundational to its tenets say, but you won't eliminate racism as a necessary consequence of doing so. It's a lot more likely, if not that likely, that you could eliminate this particular strain of romanticism than it is that in so doing it will completely rewire everyone's ideas about their societal and economic statuses and what those should rightly be.
Actually it's much easier to eradicate the romanticism if you don't waste effort trying to eradicate the racism - which you'd never succeed in dong anyway.
The key to avoiding the romanticism is to make the differences between ante-bellum and post-bellum as small as possible. After all, if everyone is living exactly the same life after the war as they did before it, then what is there to romanticise? But of course this is progressively harder to achieve the longer the war lasts. By 1865 the South is a heap of rubble, so that for a large section of the population it is impossible to just pick up where they left off in 1861. But had it ended in 1862 - - -