They were somewhat added, but not entirely. Right now, for different reasons, I can’t get on hero machine. From what I remember, the Greek one is a Corinthian helmet or a Roman Officers helmet, which both look very different. The closest thing to the Roman is the Roman officers helmet, but that looks different. The plume is different, and though it is similar, actual helm part is sort of different. As you said, we don’t have the Trojan style. It would be hard to make out of different ones, like the way it fits the face, and the open part. It also looks pretty cool.
I think out of all of these, the spartan one looks the best, and would be one of the hardest ones to make.