I was successful in obtaining my Romanian ancestors' certificates many years ago by hiring a researcher in Romania. He went to the District Office and obtained and sent me photocopies of the certificates along with his own translation of the Romanian to English for what was a modest fee.
From the Association of Professional Genealogists (APG) directory of members, one professional is listed as living in Turkey and accepts clients. Another lists themselves as a specialist for research in Turkey but lives in Germany.
There is also the Board for Certification of Genealogists, but there do not appear to be any claimed specialists in Turkish research in their membership list.
The other site that I usually try is GenLighten, which works to connect those needing help with researchers who can help them. Their search does not list any help for Turkey, but you could contact them.
Personally I would try the APG member living in Turkey. To minimize possible problems, the APG has an excellent page of tips about hiring a professional.