Originally planned to go to Czech Republic, it seems not feasible now. Is it possible to go to Poland, Hungary, Romania, and Bulgaria instead ?

This has to be asked from the car dealership. They have to agree for you to do this. Based on my experience, I almost never find a car dealership in Western Europe that would agree to this, since there are many Eastern European countries to cross on the way to Greece, and most of them are not countries that allow cars to pass through. Eastern European countries are not popular with Western Europe, and they are rarely allowed to pass through, especially Albania, Bosnia and Herzegovina, Serbia, etc. 35 days is not enough for this trip. You will be driving every day, like an overseas training. Greece is not small. It will take at least a week to play around. The key is that it is difficult to find a car dealership in France that agrees to rent out cars to drive through these countries.