http://linea-research.co.uk/wp-content/uploads/LR Download Assets/Tech Docs/CrossoverFilters White Paper -C.pdf
and it is well known in many text books that with 12 dB/Oct BW or LR filter, the phase rotation at the cross-point is 180 degree. So if you use series of 12dB/Oct filerts, e.g. series of five ( 5) 12dB/Oct filters to divide the 15 Hz - 25 kHz into five regions (including 15 Hz low-cut), the theoretical phase status in each of the five regions, in general, are;
(SL) reverse - (LO) normal - (MD) reverse - (HI) normal - (SH) reverse
Sure. I missunderstood that you're going to invert 4 out of 5 instead of 3 out of 5.
I still think you should measure phase and see what you're getting. At the end doing that is much easier and quicker than writing such long posts and you will have your measurement as a fact instead of an assumption that it is good enough.