I do not see any Gialitakis or Moschovitis in Smyrna or anywhere in Asia Minor. However, I see Mavromichalakis families.
Ioannis Mavromichalakis, son of Michael, born 1867 Smyrna, married to Marianthi born 1872 Smyrna, and his 3 daughters Anna (b. 1904), Anastasia (b. 1905) and Angela (b. 1907) escaped to Crete and applied for refugee status which was approved Jun 1922. Taking into account that Marianthi was 32 years old when Anna was born, it is save to assume that they had other independent, older children.
Also Panagotopoulos should read Panagiotopoulos (the name is Panagiotis).
The Greek letter X = Chi and not H. The correct spelling is Mauromichalakis (second best Mavromichalakis). Because many spell Greek names wrong, Mavromihalakis can be used for search purposes.