If you’re not carefull, you’ll be put in charge.
Actually, a Greek Mythology LARP would be suited to a style of RPG I used to play in called Immortals. Basically, you choose something to be master (or mistress) of. For example there were Masters of darkness, light, corruption, war, pain etc…
If someone else decided to be Master of something that overlapped your power, you lost a little bit of power. For example the Master of Night took power away from the Master of Darkness (and so did the Master of Shadow). Night, shadow, darkness etc was very popular so they all ended up diluting each other.
I mention this because the Greek gods were associated with different powers (strength, wisdom, war, death etc) and they often had children by mortals and the children inherited much of the gods attribute.
So - you could have some players (either GMs or non-combatants) who played the gods. Probably want the head GM playing Zeus. You could have players who like being the playthings of the gods playing the children of the gods and being manipulated, tricked etc. Players who didn’t want to be the gods playthings (i.e. wanted some control over their lives) would be normal mortals.
So rather than the GM/Crew/PC split we have in Mordavia, you have a Gods/Immortals(?)/Mortals split.