The white civilian population of the South are approaching levels of paranoia and fear that I think hits the point of unsustainable emotional exhaustion. The spectre of race war is becoming so real to them that, surely, many of them would have to conclude that if it doesn't strike them by the end the fighting stops, then it would have to have been made up all along.
There's a lot of danger here, with a people so fearful and ready to lash out at people who do mean them no harm, but I think there is also opportunity in the exhaustion and desperation of said people once the fighting is over, but it requires a delicate touch.
One can imagine a leader of the African-American community starting to consider at this time what the peace is going to be like, and knowing that the South is full of people who know nothing other than a hierarchy of races and have contempt of black people as their inferiors, even those that are so poor that they have no actual reason to want to support slavery. She might hit on an idea; It isn't because of Reason that poor whites support slavery, they do so because of emotion and cultural context. Southern culture submerges whites from birth into a pot of rhetoric that constantly mocks, dehumanises, and vilifies black people as animals that need to be tamed. You can't rope something in that situation into a genuine philosophical argument where your presentation of facts and logic can get through to them. What might happen if you instead changed the pot, changed the context which they are forced to operate in regarding black people?
She might be able to appreciate in ways that the male-dominated Union government can't that the women of the South are at least as important to deradicalise as the men, because they are the ones that are raising the next generation, many of them doing so on their own because of the death of their husband in the war. These women likely already have their worldview shaken by the fact that, when there was at least nothing to stop "Lincoln's hoard of Negros" from committing every ravage on defenceless southern women like newspapers have hysterically warned about for years, they ended up...doing pretty much what would be expected by a white occupying force. This weakening of the ideology they've been raised on should have pressure gently applied to it. This leader, coming from a history of learning how to draw relatively openminded whites to support abolition, might come to think that she doesn't have to go on the offensive with rational arguments about why blacks and whites are equal; for many (not all, but many), as long as they agree to keep conversing with her and treating her as a person who deserves respect, a position of racism is eventually, through a change in their habits of thinking, going to become unsustainable.
A lot of poor white women are going to be in desperate straits as a result of the war, with an economy shattered and with hungry mouths at home to feed. If the federal government decides that investing into getting the South working again is crucial to papering over the worst of radical sentiment, she might make the suggestion that programmes for women to receive support can be made conditional on them having to work alongside black women. I suspect at this point that making former confederate men work with black men is too much of an ask, and is ripe to cause a violent incident. She might take charge in schooling the black women in these programmes on what she understands about rhetoric; keep a relaxed, friendly posture, don't get aggressive, don't argue with them directly, keep cool-headed if they start hurling insults, but always insist that they remain respectful on a basic level (in any case, they're free to leave and not receive assistance if treating black women as their equals is so intolerable for them). Those white women that stick with it are likely to get their upbringing ground down by having to daily work with, converse with, and even take orders from black women. Familiar small talk at work because conversations over lunch, conversation over lunch becomes invitations to dinner at home. Even as they try to stick to everything they were taught, it'll eventually hit them that continuing to do so in the face of all evidence before their own eyes would be ridiculous.
Of course, it won't work to deradicalise everyone, and we can hardly expect every black person to have the deep wells of patience needed for such a process. But so long as it can help to put white supremacy below the critical mass it needs to reassert itself back over the South, it is worth a try. And I can think of at least one person in the federal government who would be sympathetic to its goals and its methods.
"When the conduct of men is designed to be influenced, persuasion, kind, unassuming persuasion, should ever be adopted. It is an old and a true maxim, that a "drop of honey catches more flies than a gallon of gall." So with men.
If you would win a man to your cause, first convince him that you are his sincere friend. Therein is a drop of honey that catches his heart, which, say what he will, is the great high road to his reason, and which, when once gained, you will find but little trouble in convincing his judgment of the justice of your cause, if indeed that cause really be a just one.
On the contrary, assume to dictate to his judgment, or to command his action, or to mark him as one to be shunned and despised, and he will retreat within himself, close all the avenues to his head and his heart; and tho’ your cause be naked truth itself, transformed to the heaviest lance, harder than steel, and sharper than steel can be made, and tho’ you throw it with more than Herculean force and precision, you shall no more be able to pierce him, than to penetrate the hard shell of a tortoise with a rye straw.
Such is man, and so must he be understood by those who would lead him, even to his own best interest." - Abraham Lincoln, address to the Washington Temperance Society in 1842.