I have limited experience in hones beyond 8K. I just have diamond pastes on balsa (great sharpness) and a Dragon's Tongue (smooth but not sharp) so far.

But I think in this range you are not simply improving the edge so much as tuning it to your taste.

You seem to be wanting more sharpness rather than more smoothness. For that reason I think the Shapton 16K might be better for you than the Chinese 12K.

But if you already have pastes, try putting them on balsa or a paddle strop. Similar technique to a hone, so might work well for you.