The Greek culture did not disappear during the centuries under the Ottoman rule, there is no reason to suppose it would under a rebirth of the Ottoman Empire. It did however dissappear from the Greek colonies in France, Spain etc.
Under the Ottoman system, all persons and property were technically the property of the Sultan, and all civil disorder was against his wishes, and therefore stamped out very firmly as soon as it arose. The New Ottoman Empire would therefore have the duty to impose a peaceful coexistence upon the citizens of Greece, Turkey, Kurdistan, Iraq, Syria, Israel, Palestine, Egypt etc. which would sort out a lot of the worlds problems.
The Ottoman Sultanate practised a deliberate policy of 'outbreeding', so that they contained hardly a drop of the same blood as their subjects. A number of them were clinically insane, but this was not either a prerequisite nor a disqualification for the post. They also had the traditional task of annhiliating most of their relatives.
I may apply for the job.