Gimmee a break, the Confederate military was not "integrated."

And the South was hardly on the verge of emancipation at the end of the war. There was some discussion of it, in the context that they were going to lose anyway, and emancipation was inevitable. At best, they would have been trying to take credit for the efforts of others. Wow, give them a gold star.
With imagination like that, I don't see why you aren't working on a science fiction version of the Civil War. Do the Mirror Universe Civil War: What if the Confederates were the abolitionists? Turn everything on its head, to hell with historical facts. It could be incredibly entertaining!
Meanwhile, back in the real world, there were a few scattered instances of blacks serving in the Confederate military, such as the Louisiana Native Guard, who failed to flee New Orleans when the Union Army came to town. Instead, they offered to join the North and fight for
them. I guess they were just eager to fight somebody, or more likely, they had property in New Orleans that they were eager to defend - New Orleans' "colored" population being unusual in that regard.
By contrast, the Union Army and Navy totalled about 10% black - 200,000 out of 2 million. Here's my book list for further reading of the
nonfictional role of blacks in the Civil War (some of which also cover the war in general):
The complete Civil War journal and selected letters of Thomas Wentworth Higginson and
Army Life in a Black Regiment by Higginson.
Battle Cry of Freedom and
Drawn with the Sword: Reflections on the American Civil War
by James McPherson.
Blue-Eyed Child of Fortune: The Civil War Letters of Colonel Robert Gould Shaw - the guy from
Glory.
And for a
really thorough experience, peruse
Freedom: A Documentary History of Emancipation, a series of 900-page tomes, which cover both Northern and Southern black recruitment (among other topics), and put the Southern recruitment into context - extremely sparse, especially compared with what the North was doing (and with a very different political complexion.)
And right now you can read an interesting essay by historian Ta-Nehisi Coates,
Why Do So Few Blacks Study the Civil War? Among other things, he explains the persistent oddity of the viewpoint that "the war wasn't really about slavery."
And since we're on the topic, I did notice that the cast of
To Appomattox is blindingly white. Okay, it looks like it's going to focus on the upper echelons of the military and political establishment, so that's only to be expected.
But in addition to telling that story, I would really like something along the lines of
Band of Brothers, which takes the perspective of common soldiers. That's what I'm hoping from the show in development by FOX. And if they take that approach, they better take the Whites Only sign off the production, and include not just blacks in the military but also depict the legions of escaped slaves (inexplicably fleeing the Confederate abolitionists!) who served behind the lines in various capacities, as teamsters, laborers, cooks, and hospital workers. Blacks were far more important to the Northern war effort than is generally depicted in film or on TV. Time to change that.