a general consensus has it that the American Civil War fits the bill.
I agree. The Civil War was a major conflict with modern technology: railroads, telegraph, etc. It saw the development of modern weapons such as the armored, steam-powered warship. But it was a modern war because it was a "total war" meaning it was waged against civilians as well as soldiers. The Civil War a modern war because it was a conflict between societies, not just armies. In the Civil War the ability of a polity to maintain an army in the field became a target of war, thus war was waged against civilians as well as soldiers resulting in things like Sherman's march to the sea. I haven't read much about the Crimean War, but I believe it was a war between armies, not societies. I don't think the ability of the populace to field an army was a target of war in the Crimean War as was the case in the Civil War. If so the Crimean War was not a "total war" and would not quality as a modern war.
