Thinking about this more, because I think the discussion is productive and sits at the heart of my concerns.
For me, the claim that revivalism made "the difference," and nothing else did, looks like simplistic modeling inspired by monocausal Newtonian physics. ( If we're going to roll with loose critiques of 'modernism') Part of what is missing here is the texture, complexity and "tragedy" that we find in Biblical narratives, and which I think we also find in the real history of abolitionism and Civil Rights. For example, when I look at the Second Great Awakening, I see a powerful movement of God that dissolved existing hierarchies and social divisions, and connected people in surprising new ways. (Mixed in with a bunch of other stuff, too.) However, the people who were marked out by God's activity betrayed their own call, and went on to destroy a lot of what was made. And so, God's work was carried forward by Cyrus, instead of the people among whom God had initially moved so powerfully. (ie: the union army effected abolition, not revivals.) God's agency is not restricted to revivalism, or to a certain people who were marked out by God's activity.
Here's how I'd tell this story: Sometimes people who have experienced this kind of calling from God see some aspect of the Kingdom come in their midst, but then they turn and reject it. Then, the institutions birthed through God's action shift away from faithfulness to God's activity in history, and toward self-preservation and submission to the world. As they do this, they often see themselves as the heroes preserving the true religion, and their own tradition, in just the moment that they stand under judgment from God. They've lost the thread of the story, and so they accuse "the culture" for rejecting God's call, when they are the ones who heard their calling and rejected it...and in fact, "the culture"/Babylon/Cyrus carries forward the work that God had originally intended to be done differently, by his people.
Something like this story might be said to repeat, starting on Azusa Street. Instead of getting Civil Rights acknowledged through the collapse of cooperation with Jim Crowe, or a velvet revolution driven by de-segregated churches, we got them acknowledged through LBJ. Pentecostals split largely along racial lines, and Civil Rights legislation passed in spite of opposition from the SBC...which was itself, substantially, a product of the Second Great Awakening. So I just don't buy the story that the SGA set us on an inevitable path toward abolition (and racial reconciliation more broadly), I think its ongoing legacy is far more ambiguous. I'm not even sure if its aggregate effect was positive or negative, in terms of "causing" abolition and racial reconciliation...and I'm not sure that is even the kind of story we should be telling, or expecting.
If there is any sufficient, proximate historical cause for abolition, as it happened through the Civil War, I'd have to say that the original Constitutional compromises set up a conflict of interests between the slaveholding south, and the non-slaveholding North. I don't buy that...it really isn't that simple. But it seems far more plausible than the claim that the Second Great Awakening caused abolition, and the compromises of the Constitution didn't "move the needle at all".