Yes, what you are hearing over much of the mid-range and above, is a good compression horn speaker, capable of startling detail and realism at times. I've yet to reach the limits of mine ... for instance, every amplifier change is instantly noticeable.
Do the Ks have sliding ports on the front, like the Canterburys? After much trail and error, I prefer all settings to be 'flat', which also meant one port open and one closed on each speaker. Having both closed restricted dynamics, soundstage and realism.
On your last point, I think that the biggest improvement I've heard in Tom's system was when he got Paul to custom-build some crossovers to perfectly match his cabinets/amp/room. Not a trivial exercise though, as I understand it. OTOH, the Prestige models had much improved crossovers, I believe, compared to previous models ... certainly better internal wiring and components ... so maybe not so many gains to be had, compared to the 'vintage' models? It'll be interesting to see how you get on.