First of all, I enjoyed the latest chapter; looks like the hangmen are getting a lot of work.
Regarding Braxton Bragg's hanging: considering his reputation as a harsh taskmaster, I can see soldiers and officers who served under him attending his hanging and jeering him.
As for E.P. Alexander, considering what Fiver said, that can be considered treason (or at least oath-breaking).
BTW KI, there is one group of officers who would be seriously considered for hanging: Confederate Naval officers, especially those serving on commerce raiders like the Alabama, Florida etc. Early in the war, the Union had a policy of treating captured Confederate privateers as pirates; Davis threatened to hang Union prisoners in retaliation so it was never implemented. However ITTL, I can see the US deciding to treat captured officers of these raiders as pirates; so men like Semmes etc. would more than likely be tried as pirates and hanged if caught.