"Let Us Strive" was really good, but is on hiatus.
Snake Featherston's "Up With the Star" is excellent (May 1864 POD, pretty much the way it would have happened). It has a lot around the world, too.
"The Union Forever" doesn't quite have Reconstructin per se since it's a mid-1862 POD, but it's close, with a surviving Lincoln and all, so it's still quite good.
And, might I recommend this
http://stores.lulu.com/store.php?fAcctID=53590504
“Brotherhood and Baseball” tells the story of several surviving soldiers on each side and a much smoother and (at least relatively) faster transition toward equality, thanks to leaders like Octavius Catto and Oscar Underwood.
From the back of the book.
A sudden change thwarts Lee’s miracle at Chancellorsville. As Union victories mount, President Lincoln tries to use a Southern Christian gentleman as a peacemaker. Meanwhile, two Southern soldiers and several Northern ones survive, including baseball-loving John Benton, who is determined to help the races get along as equals. He hopes to at least achieve the integration of baseball, a sport which is covered more fully in ‘If Baseball Integrated Early.”
This alternate history shows the lives of these survivors, as well as President Lincoln, Frederick Douglass, and others from that era, including Octavius Catto, an early Civil Rights leader whose survival because of baseball is another great help in improving race relations, or at least trying, in a South that holds very little animosity toward the more lenient North.
This sets the stage for an eventful 1910’s and 1920’s. President Underwood faces a crucial decision, and those same men who survived the Civil War thanks to its early end find themselves witness history again as more and more things besides baseball are integrating in the North. Can even the Southerners begin to see the benefits of an integrated society?
This and other books of mine - including the baseball companion of this one, "If Baseball Integrated Early,' at at lulu dot com. Sadly, they don't have the capacity to separate people with the same name if you click the name, but you can search for one of those, then click on "Author profile."
The baseball companion.
“If Baseball Integrated Early”
Part one is a series of short stories introducing John Benton and others. Benton is a great player who would have died in his late teens/early 20s, had the Union not won at Chancellorsville, causing the Civil War to end 18 months early. Benton is greatly involved in ensuring that the game remains integrated in the 1870s. It's a sure thing by the 1890s, and by 1901, the new A.L. allows integration.
Part 2 goes season by season, from 1901 to the present, with mentions of who played in and won the World Series, together with blurbs about famous moments, players, pennant races, and some off the field stuff, like history, effects on the NFL, etc., but most is baseball, though some is players off the field, like Satchel Paige & Dizzy Dean on Vaudeville.
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The synopsis on Brotherhood and Baseball reads:
Civil War ends early! Abraham Lincoln lives! Explore an eventful world with numerous twists and turns, as Lincoln's leniency leads to less Southern hostility toward the North. Can this and the integration of baseball from the start be enough to bring Civil Rights to America early in this alternate history? Can baseball really have the impact one man dreams? Enjoy as national leaders and ordinary people interact from the sudden Union win at Chancellorsville through the 1860s, then into the 1910s and '20s and beyond.
Pretty convergent in world history so not much voerage, though you could argue that different things happen. Mostly focused on America - baseball is quite divergent in places, though still the same recognizable game.