'...........the better gripping tires on the rear obviously increase the rear grip............'
This can actually bite you hard. If using the old tires on back, they will have a tendency to slide out at lower speeds, possibly alerting someone to a problem. The new tires will hold better then break loose at a faster speed from higher forces, a much more dangerous situation since at higher speeds, rarer and more unexpected. A car that slides out easier forces one to be a better driver unless he is an idiot. Refer to driving on ice........