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I have a problem with "old" here, this is why I didn't touch it at first. I would change it completely, as we can't say "ancient" here, nor can we say "παλιοί" because this does not bring to mind Byzantine Greeks but just those of two or three generations ago. ...
For me, a translation with παλιοί Έλληνες is not that bad. Maybe because I've lived with and known people of two and three generations ago, they don't seem very παλιοί to me.. ;) :)