Wow, this was amazing! It was a great job of showing how things derailed till the government was lost, and then having the military coup happen, even though I expected it to happen, and yet still having it be a surprise shows how amazing a writer you are.
Really, these guys look like just your garden variety despotism at this point. There won't be many lost causers in a world where their government was not even a Republic at the end. And while General Lee may be considered a martyr by some, he was ready to strip people of their so-called "property" rights to win the war. Those Confederate generals who do survive, and even those who don't but their writings do, which will be a few, are going to lump Lee in with Breckenridge in some ways because he will be seen as a traitor to their true cause. So it will be hard for even the average person to totally lionize Lee because they will have to answer about why some of the top Confederate leaders criticized him so harshly.
Plus, you have OTL where he was willing to tell his men to lay down their arms because he knew it was hopeless. That had to be eliminated for this to truly be a fight where everyone is just asked to fight to the death. Lee does not go out in a blaze of glory here, so I suspect that his reputation won't be as great as it could have been, even without other Southern generals deciding to attack him.
If it was just a skirmish, there won't be a lot of Sharpshooters who can claim it, but I agree there will be a few. However, the guns will probably be kept for historical purposes at the Smithsonian or something. So it is possible they could be kept till forensics are good enough.
The stage is setting up nicely for Longstreet to leave. The question is when.
So now that the south is a military junta, what role does the Confederate Congress play? Do they even have one? Because I can see some getting really upset at this. In fact, Governor Brown of Georgia made threats to secede himself at times, so even if he was just blowing smoke in our timeline he might be serious in this timeline. Because if there is no Congress.. well, although Georgia is represented in the junta. But there are a few states that can claim they have no Representatives now.
Andrew Johnson's speech writer: "Well, Sir, now that we're fighting a banana republic, or should I say cotton republic... well, you can claim the president's beard is ugly. That might be your only argument, though, and I don't think you can make a really long speech out of that."