Cool plans! You'll have a blast going through all those countries.
A few remarks though:
Georgia and Armenia are already pretty cold at night and snow and freezing temperatures are not far away. Unless you plan to spend winter in the Balkans and Turkey and wait until next May, travelling the most beautiful parts of those countries will be difficult. Even in May there can still be snow in the Svaneti and Kakheti regions in Georgia. I would suggest to go through Turkey and visit Iran first. Take your time, it is an amazing country. Then come back through Armenia and Georgia.
It is impossible to cross the border between Azerbaijan and Armenia directly. You can only travel between those countries with a detour through Georgia or Iran.
Your time in Iran might not be as limited as you think. Your original visa will be 30 days max. But once you are in you can extend to up to 90 days.
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