Have they really "gotten over" it? I don't think so, and I don't think their August solemnities argue that, either.
They accepted defeat, a very hard thing to do, but the occupation of Japan was very benign, and MacArthur's intendency as the first non-Japanese shogun benevolent to the point of solicitude, both for the mikado and the people of Japan, as to eclipse the equivalent administration of Reconstruction. It is true that the Japanese were more accepting of defeat, under the leadership of their emperor, than Southerners were of Yankee, and particularly Radical, Reconstruction. But they knew that they had started the war, whereas Southerners knew much more about Lincoln's intrigues and usurpations -- the illegitimacy of much of what the Republicans did, even in the administration of the North (Fehrenbach speaks demurely, in the shadow of Rushmore, of "tribunician powers"; but the scholarly reference to the roots of Roman imperial power was intended to slide gently over the heads of most of his audience, and to speak only to other historians), was acutely in the consciousness of contemporary Southerners, who never accepted the specious Republican accusation that they had been "wrong."
Reconstruction, after all, was a sectional imposition and extraconstitutional, concocted by people who had claimed as part of their cloak of legitimacy to be working for the preservation of constitutional government, whereas factional and private advantage were their palpable, real goals -- and everybody in the country with the I.Q. God gave a rabbit knew it.
Post war comparison would be an interesting topic to spend, oh... say.... 5 or 6 years studying to get the real answer to why Southern bitterness lingered so long after the war. Cultural submissiveness of the Japanese populace during te imperial reign had to have played a significant role in acceptance of US dominance - if what happened could indeed be called that.
In comparison to the post-WWII reconstruction, Southern occupation was seen immediately as a profiteering gig throughout the states of the Confederacy. Compare today's political relationship with Japan, 60 years after the war, to the attitudes of the 1930's, when even Northerners began to look back on the war as a means to establishing a Republican death-grip on US political power.