Unipolarity doesn't preclude the existence of major powers; it's just that one is significantly more powerful than the rest. Even if we accept your criteria, there's no inherent reason why unipolarity must last a shorter period of time than bipolarity. Bipolarity can end with either one of the poles surpassing the other or a third state becoming a pole. Unipolarity can only end through the latter mechanism. The rise of countries is not a fast or certain process. It will be decades before we really see the end of unipolarity.
I should also note that in bipolarity, everything is a zero-sum game. That makes cooperation incredibly difficult to achieve. So even if there isn't war (though there have been plenty of wars in pre-20th century bipolarity periods), there is no stability either. The zero-sum nature of interaction increases hostility, which makes countries more likely to use force.
Here's a good work on the subject: http://www.jstor.org/pss/174077 The current consensus in IR is that polarity doesn't really matter, by the way.
Okay, I'll accept your expertise on the matter. Thanks for the source.