Sadly, it just means I have to develop even better technique on the stones I have
Insightfull and wise!

There is nothing else left to say. A GS 16k is a nice finisher, as is the Naniwa 12k.
Both are no "ultimate" finishers, but very good ones.
If you really wanted to add to the 12k finish (and we´re talking nuances here)
you might have to work your way into super expensive naturals or super expensive synthetics like Shapton 30k.

Have you tried diamond or chromium oxide on felt or linen to improve the 12k´s edge?
Maybe that´ll do the trick and give you that last 10 per cent