I'm a greek Cypriot and I did a similar trip this July from Bournemouth to Armenia flying through all the countries you mention, also in a single but Jeta1.
I can help with advice on airports etc but not routes as we flew IFR airways pretty much all the way.
We went from Brindisi in Italy to Thessaloniki, Albania wouldn't allow overfly at all so we tracked south to avoid, There was no issue crossing Thessaloniki to Izmir at all.
I guess that if you won't get permission to fly Vfr turkey to Cyprus but again it's just a guess, the trip is great. Enjoy
