You can work with scratches!
When I thin my daily drivers, I feel compelled to go through the process of refinishing the blades. I do a brushed finish on the flat of the blade, and a haze on the bevel. Getting a good satin brushed finish can almost be as maddening as any other type of polish. It depends what standard you hold yourself to!
Before getting to the brushed finish, you can polish the surface to the final grit level you want, or even one git higher. At that point I have found good success doing more or less what
@lemeneid said. Knife below and abrasives above. Put the aesthetic scratches on the blade by doing very controlled passes across the surface. I even use ruler to ensure I am keeping the passes straight. The lighting in this photo is super harsh and revealing:
View attachment 87703
This is the front quarter of a 210mm gyuto. The brushed finish is as straight as I could manage! Drove me mad... had to do many resets. On average I would consider this finish to be 70% perfect. Suits me fine. Again, it is a knife that is to be used. It is a dirty 5000 on the core steel, a painfully done 600 grit brush on the face and a dirty fingerstone finish on the bevel. It looks quite different in normal lighting. The brushed finish is quite bright and shiny, the bevel is a nice dull kasumi and the bevel is mirrorish. There are some nice contrasts.
On uchigumori (bench and finger stones)... Sword polishers have a collection that they can match to the steel they are working with. As
@nutmeg pointed out, yours is likely too hard. It is easy to get hung up on tradition. Anything that gets the job done is fine by me! You don't
have to use uchigumori . As you noted in your previous post, you may find stones better matched to your knife. I have a Shobudani stone that reliably leaves a lovely scratchless kasumi finish. It may be too cloudy for hamon though. Experiment with what you have in your tool kit!