When an orchestra is playing on stage, isn't the resultant sound of several cellos, tubas and string basses (and everything else) a "phase coherent mess"?
The sound waves of an orchestra are not like the photons from a laser all the same wavelength and exactly in phase, but they are nevertheless additive in the totality of what we hear.
I'm sure you understand that to add post-recording phase shifts (via one's system) would obliterate the beauty of an admittedly phase-incoherent performance. With a wonderful system like yours, it would be easier to hear the effects of improper phase. Perhaps you could make some temporary adjustments that would allow you to evaluate the effects of phase shift between your towers and subs????
Lee