It may be difficult to find a car rental that will accomodate your wishes. I did some research through AutoEurope, which gives great driving guides, that are harder to find with companies like Avis, Budget, Hertz, etc

I checked for some of the countries that you mentioned: (nothing was shown for Albania, at all). Information from AutoEurope stated:

Cars rented in Hungary are not allowed into the following countries:

Albania, Bosnia, Belarus, Bulgaria, Croatia, Estonia, Greece, Latvia, Lithuania, Macedonia, Montenegro, Russia, Turkey, Ukraine and Yugoslavia.

NOTE: For an additional fee, travel into some of the aforementioned Eastern European countries may be arranged for specific car categories with advance notice.

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Cars rented in Bulgaria are not allowed to be taken outside of the country, exceptions may be granted for an additional fee. Additional insurance may also be required when traveling outside of Bulgaria.

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Cars rented in Romania are not allowed into the following countries: Albania, Bosnia/Herzegovina, Croatia and Slovenia.

I would suggest starting with AutoEurope.com or AutoEurope.ca (for Canadian) residents) , check into the driving guides,and what exceptions they mention that can be made for travel into all the countries you wish to visit.