I read both your articles - this one and the previous one containing more historical examples - and if it weren't for two issues (one relatively minor, one major), I'd have to agree wholeheartedly with you. Before I continue, my compliments to your breadth of knowledge of history, culture, and religion. I sincerely look forward to your articles in the future.
The major flaw in your argument is the fact that unlike every one of the examples you offered, the South was fighting to preserve the institution of slavery, their "right" to own slaves. For all the examples you presented, slavery was a normality, a condition unworthy of political debate. But for the South, slavery was the raison d'etre of both their secession and their war.
For that reason, the Confederacy would be more accurately likened to Nazi Germany than to the Roman Republic (or Empire).
The relatively minor flaw is that there were two periods that saw the overwhelming majority of construction of Confederate monuments: during the rise of the KKK and Jim Crow laws, and in the period immediately following Brown v. Board of Education (which period also saw the formation of the "segregation academy system" which I attended for a year). This certainly implies the motivation was less to glorify great military leaders and much more to "keep the Black man down".
If it weren't for these factors, I'd have to agree with you.