I agree with your general approach: First establish some criteria for hegemon legitimacy, then assess various candidates against those criteria. You could add more, e.g. Corruption Perceptions Index. Over decades the Russian government has demonstrated poor performance for the people under its control, thus it forfeits its claim to a larger "sphere of influence". In fact, it's a big лохотрон. Pax Americana, on the other hand, has been of enormous benefit (which is not to say that it is perfect). People like to cite Vietnam and Iraq, neglecting South Korea.

BTW, I'm a former treaty inspector in Russia and Ukraine, early 1990s, currently in Berlin.