All speakers require careful matching with power amps or receivers in order to achieve positive results. I have used B&W 800N series for years with 150 watt tube amps, and have absolutely no problems driving them with these tube amps.
The Kevlar cone in the 802 and 800 N series are really organic sounding when matched correctly with the right components. I thought the differences between the D series and N series were minor except for the same issue you raised regarding the D series not sounding as organic. So, I forgo the opportunity to upgrade to the D series.
Your description of the sound levels of the B&W 800 series is characteristic of what many experience when these speakers are not matched properly with the power amps and are not positioned correctly in your listening environment. The 802 is larger than the 805 and might require a different speaker placement due to the wide dispersion characteristics of the nautilus tweeter and Kevlar cone Mylar enclosed midrange section.
Finally, how are you connecting the speakers to the amps? I see that the 6900 offers various ohm taps for speaker connections. Have you experimented with using different taps? How about bi-wiring? Are you using regular pairs of speaker wires from the amps and then connecting to the speakers and crossing the mid/high and low/low with speaker crossover cable or B&W factory supplied blade on the 802's?
I am using the 4 ohm taps for the mid/highs and the 8 ohm taps for the low/bass sections on my 800's. The amps I am using are the MC2301's, 300 watt Mcintosh tube amps. Some experimentation is required to configure almost any system to get optimum results, no matter the brand. I love the looks of the Nautilus series and so does my spouse, as we do the sound as well, so, replacing speakers was not an option, replacing amps were the reasonable option for us. The last solid state amp I owned, the Bryston 4BSST's, had a pair of them driving these speakers in bi-amp configuration, gave the best bass I ever heard from a speaker. Movies were just amazing and dialogue was great; however, for music, the Bryston's seemed a little dry compared to the organic sound of tube amps from the likes of Einstein and Octave.
Good luck,
Audioquest4life