In this ATL state death theory is accepted and a majority black state based on the Mississippi Delta is created. Lincoln, who not only evolves on the state death issue due to his lack of better options to keep the peace in the south along with a desire by 1865 to give Black Americans some type of political franchise, does not get assassinated and works with Radical Republicans in the weeks after the Civil War to create this new state of Delta. Lincoln is given extra political capital after he escapes assassination but the Vice President is killed in the plot.
In any case Congress creates the State of Hamilton which due to its overwhelming black majority population is the bastion of reconstruction. Many of the Blacks who in OTL went west after the war go to Hamilton. The state's constitution is written by a supermajority of Black Republicans. The State of Hamilton mandates (relative) egalitarianism on the basis of race by law and has NO Jim Crow or Black Code laws.
Anyway this sparks a white reactionary backlash much larger than OTL but also less effective. The KKK and other terrorist organizations CAN'T dislodge the State of Hamilton's government due to continued federal support. Many of the wealthy white landowners who provided support to the Klan are imprisoned, stripped of their land and it is redistributed to the state's poor, black and white. Basically a half assed land redistribution campaign occurs that is far more effective than any we saw in our universe.
By the 1880s no matter what political butterflies Reconstruction in the south is a dead letter and white Democrats have retaken control of the state governments, EXCEPT Hamilton. In Hamilton the land is largely out of the hands of the former planter class, many of the lower class white population has fled but many blacks from the Jim Crow south have taken their place, a Black run state government exists with Senators, Congressmen and clout in the Federal Government. The state has a majority black militia that has sometimes fought with out of state groups (having long ago crushed the internal reactionary white population), has black juries and has a mostly black population with the same colored people in local, county and state government to boot.