The challenge is to have the Greek monarchy get abolished, and stay abolished, earlier in the 20th century, specifically by January 1946.
Rules:
1) Greece cannot become a Communist dictatorship or Communist one-party state
2) Greece cannot have a right-wing strong man with the regime longevity of Franco, Salazar or the Shah of Iran.
3) Greece cannot be occupied by foreign powers for more than 10 consecutive years.
I think the above eliminates some of the easier solutions to the OP.
Go.