No guarantees. I'd bet a fortune you are bottoming out the mid/woofer drivers.
I own Michael's Raidho D2 loudspeakers and what you describe is exactly what I might hear if I had the music program amplified to high for them. Everything sounds great and then "POP" or multiples. It's bass and a small cones can only go so loud.
I have a class D amp with 1kw into 4ohms and a 2000 damping factor so I do not blame the amp. I know I need to high pass but they go to 30 in room on their own. I just try to watch the volume levels (mid 80s for me).
I imagine those X2s are fabulous in most every other way. Classical music is pretty tough when it comes to intense transients. Consider high passing the Z2s a bit to relieve the ultimate low end and adding sub(s). Good luck!
Those ribbon tweeters Michael designed are the best I've owned. I had a pair of small Scansonic MB2.5s (by Michael) and even that slightly 'heavier' sealed ribbon tweeter bested the Dynaudio Esotar 2 I listened to on a pair of Sapphires I owned for five years. I've never heard 'distressful' noises from them, just silky treble...