That sounds like a really useful book! Adding it to my TBR. The focus in The Thin Light of Freedom is much more on what's happening on the ground rather than in congress, so Capitol Men will almost certainly have loads of different material because the focus is so different.
The thing that gets me about the what-ifs of Reconstruction is that, in order for Reconstruction to work, southern whites would have needed to be less stubbornly attached to their white supremacist beliefs and their desire to keep their social structure as unchanged as possible (they conceded that slavery was over, but that was absolutely their only concession to change) - but if these imaginary less-stubborn southerners existed, there would never have been Reconstruction because there never would have been a Civil War in the first place, because they would not have thrown a hissy fit and seceded after Lincoln's election.
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The thing that gets me about the what-ifs of Reconstruction is that, in order for Reconstruction to work, southern whites would have needed to be less stubbornly attached to their white supremacist beliefs and their desire to keep their social structure as unchanged as possible (they conceded that slavery was over, but that was absolutely their only concession to change) - but if these imaginary less-stubborn southerners existed, there would never have been Reconstruction because there never would have been a Civil War in the first place, because they would not have thrown a hissy fit and seceded after Lincoln's election.