Hi, long time user of the Beyma XA's here, 15XA38Nd in my case.
The XA's sure are controversial drivers. The raw LF and HF drivers measure not very nice, let alone directly on axis, its design is based on HF diffraction to increase HF coverage angle, after all... but IMHO coaxial should never be used and characterized fully on axis where full symmetry only exaggerates everything. Distortions are OK level but nothing special.
With DSP XO and full DRC (+sub) I found they sound quite amazing, though. Clearly not exactly truly natural / neutral but a ton of fun to listen to, there is an increased "dynamic and timbral structuring" that found quite addictive (even if it might be "fake" resolution). They can get a bit rough but are honest to the bone in what they do, so to say. Subs are essential IMHO, the LF cone movement should be restricted to only a few millimeters of excursion. Then again, with the 15" in a large ported box you won't feel the need for a sub ;-)
Lining the compression driver's back chamber with thin felt reduced some HF resonances, and I also tried to damp the ringing phase plug assembly (die-cast parts) with small pieces of stiff rubber. A friend of mine has coated the LF cone with some laquer to reduce/damp breakup to some exent. I woudn't go as far as the guy in the link of post #17 and redo the diffraction ring for less diffraction, I'd rather start from a standard (low diffraction) coax like a Tannoy if I wanted something smoother (which I did in the end).