Status update:
Went to the dealer, yesterday (yes, he came in for me on a Sunday...), bringing along a selection of discs that would sound awful (remember: when played at low volume...) in the context of my system / room.
His configuration was non-Naim electronic. IIRC Lindemann Player (which is stunningly good, also heard that in other locations, 8000 USD range) Esoteric pre (in the 4000 USD range) Pass 350.5 amp (in the 10000 USD range), Transparent speaker cables (in the 1500 USD range) and of course the Summits. Down to listening levels where the "ambient" hiss was drowning the music, piano music came flowing out of the Summits as expected: Crystal clear, without even a trace of disortion, sounding like a piano with voluems turned down (what a surprise !). When played loud, the overall characteristics of the system were different to what I'm used, of course, but - hey - not bad. NOT bad, at all. (Again: Remember, that I had a whole Saturday in his studio where the Summits were connected to a Naim system, so I can compare).
He gave me speaker cables to try (Supra Sword including the bi-amp bridges), which didn't change a thing in the trouble area, when I tried them at home.
Next step will be getting a different amp (I'll give the Pass a roll...) at my home, and then make decisions based on the result.
Stefan