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Yes, phase-unwrapping means taking the allpass response of the XO (also known as the excess phase), inverting it in time and use it as convolution kernel to undo the original allpass behavior. The system now behaves like a single way with the same magnitude response. No ringing at all, at least on the design axis, as noted. By design, literally.
Assume a simple crossover at 1kHz with ideal drivers (infinite flat response from DC to light).
Let LP(s) be the original lowpass and HP(s) the highpass. LP(s)+HP(s) form the system sum which is an allpass AP(s).
The time inverse allpass be denoted as IAP(s). It is immediately clear that IAP(s)*[LP(s)+HPs(s)] is the same as IAP(s)*LP(s)+IAP(s)*HP(s).
Well it's hard to argue with the maths: I stand corrected