Reverse polarity

I'm assuming that what you mean is that you have reversed the polarity of the high input on the back of your speaker in relation to the low input.

If the crossover point is low enough it may be that you are simply putting the bulk of the music into absolute phase.

Another possibility is that you have some room resonances at the crossover point and by reversing the polarity you are getting a dip in the frequency response at the crossover point that helps to limit the room resonance.

As an experiment have you tried leaving the highs reversed and then also reverse the lows so that they are both "reversed".

Your speaker cables may be labelled improperly. Also, try this; listen to a song that normally has the vocals as a centre image in between your speakers. Is it still in the same place?

Check polarity with a battery.
http://www.soundspeakerrepair.com/speaker-parts-cp/Speaker-Testing-with-9-Battery/INST/Installation+Instructions/

What happened was my amp came back from upgrading/repair and 1 of the up grades was new Cardas post and I got them backwards cos they are not marked for multiple taps so I looked at a few pics on the net and found out they were reversed.