the soundstage is just too low and small and sounds strained at high volumes.
I don't doubt you are using premium quality amplification in which case either
1) You may need a sub - to fill out the LF.
2) The midrange and tweeter are compressing somewhat at the levels you like (Classical is the toughest form of music for a speaker as it has the most dynamic range - and needs to be cranked to sound loud where as pop/rock can sound loud on mini-pc speakers)
I think point 2 is most likely based on your comment about "strain" - that tweeter is working down to 1.75 Khz - as in most two ways if something is to give then it will be this tweet as it starts to compress (driver excursion increases dramtically as you do lower in frequency). This is a quite common problem with beautiful sounding audiophile two ways...they typically make the tweeters work too hard - so at elevated levels they get strained. You get utterly fantastic sound and great imaging and fantastic dispersion (dome tweeter) from these two way designs but you don't often get great dynamic capability....and guess what => that is why Kharma make the bigger models for customers with large rooms who want that great Kharma sound but find they strain/stress the smaller models!
A properly amplified line array may do it for you, however, so would a good three or four way speaker or a D'appolito design or a pro design with pro drivers. Your speakers are beautiful so I would suggest an aesthetic speaker designed for a dynamic presentation - like big Wilsons, Egglestons or the bigger Kharma designs (which use Appolito which has TWO midrange drivers to get over the driver compression limitation at extremely high levels - no strain!).