I’ve heard it all my life and “The War for Southern Independence” was used extensively by politicians and newspapers, “Ive also heard and seen in print “The War Against Northern Aggression” all my life and it probably didn’t come into use until after the war. Some of it’s origins are attributed to the fact that the “Cause” hadn’t attracted great numbers of enlistments, enough to fight a war until President Lincoln called for 75,000 volunteers to invade the South. It has always been known in the South that for many of those who participated it was not political. And yes I did make the statement with a degree of tounge in cheek, the same way I often ask a newcomer from the North if he’s a yankee or a damn yankee, this is part of our history and with it came great suffering and hardship of our people. The women of the South were bitter and held grudges for generations beyond the years when the vetrans of both armies would sit together and share stories. There were atrocities commited against the civilan populations, an example would be the shelling of the civilan population of Vicksburg as well as the shelling of yellow flag marked military hospitals in Vicksburg. I’ve not commented on slavery, secession, then or now, but only something that may offer a little insight into how this Southerner views the history of the war and the aftermath. Many of us had ancestors who served in this conflict and while most came home all didn’t and none including the civilans were unscathed.
I thought it was something "Senator Cleghorn" the radio comedian came up with that some people took too seriously, but sure, it's possible that some Southerners actually used the phrase before the joke started circulating. Given the depth of bitterness after the war, it's wholly likely that some Southerners did use the expression in deadly earnest before somebody thought up the joke.
But now some people actually believe that Southerners who experienced the Civil War actually called it "The War of Northern Aggression" or "The War Against Northern Aggression" while they were fighting it. When you wrote "In the North it was The Civil War, to the Southern media and politicians it was The War for Southern Independence, to the those in the South who did the killing, the dying and the mourning, it was The War Against Northern Aggression" it certainly leaves that impression. But that isn't true. As you say, it was something that most likely came into use after the war.
The people who actually fought the war were less bloodthirsty and warlike than politicians and newspaper writers who didn't see action. That's true of most wars when people are actually fighting. Afterwards politicians and journalists may want to forget what veterans can't.
Also, when you're fighting a war you also don't have the time or the motivation to overthink things the way that people do after a defeat. There are more important things to do and to worry about than playing word games.
I don't have an opinion about the rest, except to say that it all happened a very long time ago.