With some speakers, you can't really do much about this. A lot of the time the tweeter harshness comes from the fact that the tweeter is high passed too low. Often, playing 2KHz and up with authority is just too much to ask from a 1 inch diameter tweeter. If you run active you can high pass your tweeters higher and sharper, but this will not work well if your mids can't play upper mid range well. Some supposedly "high end" mids (ID mids, Dayton Reference) are not meant to play above 2KHz for example, pretty much requiring a high end tweeter. By the way, a lot of Focal crossovers come with advanced crossover networks. At very least you should be able to select tweeter attenuation mode (0dB, -3dB, -6dB etc).
My HAT Imagine speakers produced ear piercing upper midrange once the volume is up to make music audible at 70mhp simply because the high pass filter with a 6dB slope in their crossover network was not enough to calm them down. Now I got hold of an active crossover, and the tweeters are set with high pass at 6.3KHz and 12dB slope, and they sound fantastic. The HAT mids do have a reputation for a good upper end extension, so I can still hear upper mid-range without tweeters playing much of it.
What makes tweeters sound bad when they are high passed too low is often the _distortion_. If this is the case, I don't think having them out of phase will help much. Whether in phase or out of phase, distortion is distortion.
Of course, another issue could be that tweeters have low distortion even at high volume, but the crossover does not attenuate them enough. If you can, try to move tweeters far away from your ears, maybe into kick panels if you have them.
There are also the "crossover geek" ways of calming down the tweeters. You can potentially do this by inserting a capacitor or a resistor in-line with the tweeter. A capacitor creates an additional 6dB high pass filter with cut frequency that depends on the cap value. The resistor I believe is for attenuation.
