To start, almost everyone thinks that for Greece to follow a autocratic path you need to lose against Bulgaria, but instead you can do it by promoting the monarchists during the referendum, but at the last event you decides to rig the election in support of the republic, thus causing a massive public uproar
This gonna provoke a popular coup under Ioannis Metaxas, the Greek autocrat at the time in OTL who became famous to resist to Mussolini
The expansion of Greek lands is considerably easier since you became Pat Aut you are able to create casus bellis in less time.
Politically speaking, basically you are a constitutional monarchy with the power concentrated in the King, on the aristocracy and on the military, think of post 1906 Russia. You get the option to go for a benevolent dictatorship, something like Dmitri Romanovich Russia, Vargas Brazil or Ferdinand Bulgaria, or to a iron fisted autocracy, of which the best parallel I can make is OTL Salazarist Portugal
Going through the Iron Fist route you are able to mobilize even more manpower, making things easier for Greece since it is their main debilitation. This route also has more PP than the normal monarchist one and the only lowpoint is stability, that can be increased with PP, so you have the damage control.