I believe the fact should be respected that an American President expressed a true Biblical precept that was well recognized and accepted by Christians in general in his day and that he was one of many Presidents who understood and quoted the Bible as guide to the nation back in the day.
It's interesting in itself, but it's not really evidence. Julius Caesar thought he was under the special protection of the goddess Venus --- and he won. Hitler thought that he was following Jesus --- and he lost. Muhammad thought that God was telling him what to do --- and he won. The Catholics in the sixteenth century and thereabouts thought they were doing God's work by fighting against Protestants --- and sometimes they won. The Crusaders thought they were doing God's work by crusading --- and they totally lost. And, of course, the Confederates thought that God was on their side. All theists think that God is on their side, and all theists think that God must have wanted the war or it wouldn't have happened. So it's not particularly evidence of what God was thinking to quote what Lincoln thought on this subject --- even though he won, and even though we're rooting for him.
The only thing I claimed the beliefs of Lincoln and Jefferson were evidence for is that God's judgment on nations was standard Biblical theology ...
Well, if you like. Though it would be hard, I think, for you to prove that Lincoln and Jefferson were standard Biblical theologians. If you just want to prove that "God's judgment on nations was standard Biblical theology" then you might cite more standard Christian theologians.
But if you want to prove that "God's judgment on nations" was the actual cause of the civil war, then you need to do better than that. You need to prove that that's actually true. This is a long way from proving that Lincoln thought it was true.
So it may be true that that's what Lincoln thought, but what Lincoln thought has nothing to do with it. Lincoln may have been wrong, like Hitler and Julius Caesar may have been wrong. His opinion isn't evidence.