After learning of VMPS and reading the webpage, and also doing lots of general speaker info learning on the web this past month, I was shocked to learn that nearly all speakers wire their drivers in alternatingly reversed polarity.
I tested out my speakers in various ways and came to the conclusion that they all indeed obey that law. My Bohlender-Graebener Z-series speakers, which are essentially 2-way, have positive polarity woofers and reversed polarity tweeters, crossed via a 2nd-order Linkwitz-Riley network. My Infinity Kappa 5.1 Series II speakers are 3-way, have positive polarity woofers and tweeters, but negative polarity midranges. I don't know what kind of crossover they use but I suppose they must have even-order networks of some kind.
I had tried to play all my speakers simultaneously before with the same source signal for fun, but the result was very weird sounding, and so I stopped doing it. This morning though I decided to reverse the global polarity to all my BG-speakers and then try playing them simultaneously with my Infinities...and WOW the difference is humongous!!! As expected, I suppose. Now they play together well. Kind of cheesy but fun I guess.

Now the question for me is: should I leave my BG's in reversed polarity permanently? They are wrong either way...so which way is better? Is it safe to play them that way forever?
The Infinities should definitely be left as intended. Only the couple octaves of the midrange will be inverted which is not too bad. Midrange frequencies tend to be steady sounds anyway (fundamental frequencies of human voice, orchestra string, etc....mellow sounds) so maybe phase information of that isolated driver might be less important (on the other hand it will still be bad when superimposed upon the inverted harmonics coming out of the tweeter). Woofer kickdrums will bang out properly, and metallic clangs and sharp striking notes out of the tweeters will spike in the correct direction.
But I dunno what to do about my BG's. If I want to listen to them with my Infinities I have to wire them in reverse but that's just a gimmick. For serious listening what matters is how they sound alone. Which is more discernible to the human ear? Should woofer kickdrums bang out properly but tweeters suck in....or should the woofer kickdrums suck in and the tweeters clang out?
I am not sure yet if I can tell the difference in global speaker polarity. I *think* that I can, however until someone blind tests me I can't be sure. I grew up listening to positive polarity tweeters...and that is all that I listen to when I listen to music. I always equalize bass levels as low as I can. So I think I should reverse the global polarity. But will my woofer cones sucking in all their life will cause them damage?