It is interesting to see that so many people are convinced that more leniency equals worse racism. Certainly, there was a lot of racism in the south, but do people truly believe that you can stamp it out by force? That enlightenment is delivered at the point of a bayonet? Such methods usually produce averse effects. I suspect that if the radical republicans had gotten their way, the south would have become a far worse place for everyone. A cesspit of racist militias, far more widespread than they ever were IOTL.
J.D.Ward makes in interesting point, comparing such a situation to Mugabe's Zimbabwe. Especially if you compare what Mugabe did to Zimbabwe and what Mandela did for South Africa. In both cases, there was a while elite abusing the black population. Mugabe's reaction was one of vengeance, murder and mass exile. Mandela's reaction was one of forgiveness, compassion and attempts to embark on a whole new road... together.
If the north had approached the south the way Mugabe appreached his country, the results would have been much the same. If there is one thing history (and alternate history, for that matter) teaches us, it is that when we have to make a choice between a ruthless approach and a kinder, gentler way of dealing with issues, the latter is nearly always preferable.
My suggestion for a better reconstruction: education is key. Educate future generations, so that they learn to think critically. That way, they can leave the past behind them, and a legacy of hatred is no longer passed on. You see the same thing in South Africa: older people are often still shockingly racist. Not even out of any real malice, but because that sort of vile nonsense is what passed for a 'normal' worldview when they were young. Younger generations, growing up post-apartheid, have left those prejudices far behind.
So if you want a reconstruction that is both smoother and more effective? Don't look to Mugabe for inspiration. Look to Mandela.