This is a really neat idea! It's super exciting to see people getting into research and conceptualizing; I'm so glad you're having fun!
Regarding Melos, I highly recommend checking out a bit of Thucydides' Melian Dialogue if you're up for some reading. It's essentially a dramatization of the negotiations between Athens and Melos leading to Melos' sacking. It offers a lot of insight into philosophical and political motivations that might be of interest (political realism and idealism are put literally into conversation; Athens employs a lot of "might makes right" rhetoric; there's some debate about piety, what the gods favor, what natural law entails, etc) and could help flesh out some historical context.
As for the Antikythera mechanism, man, that thing is cool. It's an incredibly interesting, sophisticated artifact (the first analog computer!) that I barely even understand, but you're right that it's a bit anachronistic for Melos. You might even have ideas for more than one game or musical piece here!
Whatever you make, I'll be looking forward to it!