I don't know what your take will be, of course, but here are some of the points I've found to be important over the last seven years:
1. I avoid the use of the term neo-Confederate, since the neo-Confederates were successful in their effort to rewrite history over the last 140 years, so virtually all white Americans and even some Europeans believe the fiction that the Civil War was not in fact about slavery, at least not largely. I therefore call the people who attacked me "supporters of the founder of the Ku Klux Klan", or even just "Klan supporters". This is accuate, as neo-Confederates will not disavow the Klan. One website telling people to write the chairman of Vanderbilt's math department explicitly said the Klan only protected women and children; and at a meeting attended by Vanderbilt spokesman Michael Schoenfeld in 2002, one man in the audience stood up and said the Klan only defended Southerners. I was the only person in the 100-person meeting to object to this statement. I believe a woman who does research on the United Daughters of the Confederacy (who teaches in North Carolina) was one of the speakers, as was Schoenfeld.
2. Neo-Confederates trick ordinary people into thinking they represent Southerners---as if black Southerners don't exist---when in fact they don't represent even white Southerners. Hence, an editorial could be published in the Vanderbilt student newspaper entitled, "Ability to Teach?", questioning whether I could teach white students. (I believe the editor's name was Alex Burkitt.) Another article could be published by Jacob Grier claiming that I gave white students lower grades as a form of reparations. (On his website Grier now labels this satire, but the article was referred to by the Nashville Scene newspaper.)
3. The neo-Confederates are terrorists, using a textbook definition: they intimidate ordinary people (reporters, third parties) into agreeing with them---or at least into not criticizing them---with the threat of violence.
4. Their modus operandi is to call the few people who do disagree with them crazy---in other words, they use ad hominem attacks. (Of course, they also write spurious articles where they make a large number of bogus historical claims, the latest being that lots of blacks fought with guns on the side of the Confederacy.)
5. This is a fine point, but (a) while I agree with you that the Confederates should have been executed, (b) I would have considered it an honor and a duty to carry out the sentence myself had I lived then, (c) if I had been transported back in time into the midst of a group of Confederates, they would not have hesitated to murder me, without even a trial, (d) if they could have get away with it, the neo-Confederates would murder me now, including the ones who pretend to be more "urbane", in fact I did not write that the Confederates "should" have been executed, but merely that they committed a capital offense, treason. (It is irrelevant whether or not the Confederates believed themselves to be committing treason.) This is an objective, and true, statement, and I had hoped in this way to avoid a possible objection to my essay. But maybe it's a point worth stressing.
6. If current or former Vanderbilt administrators want to make it clear where they stand, they are welcome to state now, in 2009, in no uncertain terms that the founder of the Ku Klux Klan was an evil war criminal and that the Confederacy was itself evil.