The one thing I'd ask then - how would you approach this education issue?
In a general sense, I mean. From the standpoint of Reconstruciton, even those who wanted the new amendments accepted were generally lukewarm at best on "equality" - so I imagine any such program in the world we have to work with would be relatively puny.
But it couldn't have hurt to try to cement that the new order was a step forward, instead of just an odious annoyance.
One of the major problems with "democracy" in the South, as I understand it, was that it was inherently limited to the select few. Uneducated non-landowners, regardless of race, were generally shafted. This partially fits in with (though is a perversion of) the basic idea that only the educated citizen can be a good citizen. An idea that was present in American republicanism from the outset, both in the North (the generally Federalist financial elite supported it) and the South (the planter elite supported it).
Now, if somehow the Radical Republicans can be convinced that reconstruction has to truly be about constructing a new America (a more perfect union, needed more than ever), one ideal way to do that would be to ensure that all (or more) citizens became educated citizens, instilled with republican values.
For the poor whites of the south, it would free them from the planter yoke and make them less vulnerable to bigotry stemming from a general lack of education. (After all, proven fact: the more educated a population is, the more tolerant it generally becomes.) For the black population, it would mean that they could truly be independent, rather than being forced to return to the plantation and work for a measly sum under still terrible conditions.
In both cases, it would mean that the power of the planter elite would be broken without actually having to fight the planters at all (or much, anyway). The poor, undeducated people they could previously use and exploit as foot soldiers and cannon fodder (be it in a war, or in a racist militia) would become less and less available to them. Economically and socially, educating the poor makes perfect sense as a way to break the power of a corrupt elite.
As for how to do it: they could just dig up a proposal orginally made by Thomas Jefferson in 1781(!), to build schools in every county, where all children would receive an education at public expense. The top 10% of every class would receive further education at a district school, and the top 10% of those would receive funds to attend university.
And make the schools mixed/integrated from the outset. Black kids and white kids in the same classroom. Yes, there will be trouble over that. Yes, there will be hatred and violence. And yes, that's where you have to be tough and crack down relentlessly.
But a generation or two later? The disease of racism will be fading away already, dying with the old generation. The South will be on its way to a healthy economy, instead of a slavocracy. And America will be the better for it.
You said it right in your previous post: Lincoln could have done it better. He was the kind of man who, when presented with an approach like this, would have gone for it. It might have even been enthousiastically embraced by the Radical Republicans. After all: this, too, is radicalism. Just of a different kind.