I'm sorry for the unpleasant experience you've had with him. I think you've done a good job in keeping your cool, remaining professional throughout that ordeal. It was also great that you've apologized for the inconvenience he felt, and asked if you could help him in order to calm him.
It didn't work, and he kept on being the hole that he is, but you did what you were trained to do. And though you did not receive any tangiable form of justice, your kindness and patience made him look bad before everyone.