With a DMT 325 or 1000k sand paper, or by rubbing the turi on the surface till all the dwarf comes out of the stone. I wouldn't obsess about having 100% clean surface, but you do want to clean it from time to time.
I think you may be using too much pressure on the blade, to get all that swarf on the Nani 12k. I do get some light swarf on my 16k Shapton glass but it is easily washed with a rinse. And after several razors, it may need a light lapping.
This is a shot in the dark, but try 10-15 passes with very very light pressure on the edge of the blade. Make sure it is moving water all along the edge, with the lightest pressure you can. Then strop linen and leather and see if it pops hair. Even if it doesn't, try shaving with it ( have a backup, in case you need to bail). After that, I think, you will be able to know if its close or far. If its far from shave ready, you may need to go to a lower grid stone. Do you have other lower stones? Other wise, send it in to be hone.
A shave ready razor that needs a touch up, at least in the Shapton G 16K, only requires 6 to 15 passes at the most. Don't know in the Naniwa, but start with the less than more.
The thing about using too much pressure is that it destroys the sharpness of the edge. Too light a pressure and it would not move water along the edge.
Don't give up, we all been there. I gave 30-40 passes first time I touched up a razor. The edge looked like a saw under the loupe. Good luck! Double O