I have tried about 2 months ago to test some sword polishing techniques. Damian Kordic was very kind to show me the basics.
I have done 2 knives with that technique and then go back to my own one, as I did not get the results I wanted.
What I learn : It is very hard to control and be sure you're not overgrinding the top of the bevel. Mostly because I am making knives with kurushi/hammered part on top of the blade, the shinogi is not set as a perfect line but is moving with the differences of thickness of the blade. So I was overgrinding that shinogi part, did not see I was overgrinding and when I get to finer stones I could see the stones were not touching the all bevel.
Normally, sword polishers are not grinding everywhere like from heel to tip, but they look at the blade, find the high spot or high area where there is too much material, select it and grind only that part, then look again, etc... I did not succeed to do that. It needs... eyes! it needs to know what to look at, find the subtle change of light because in some place there is too much material.
Must be little bit easier with a full polished blade compare to a blade with kurushi, maybe.
What I could see was that with the convex shaped stones + the way using them, the technique could grind very fast. For sure faster than flat stones. And the blade even with san mai, get bright so you really have a nice view on scratches and bevel shape.
The main problem of that technique is not a problem but a knowledge : you need to practice again and again so you have eyes to see your blade and see what to do looking at it, before you grind it. That need experience and knowledge, years of work. It is powerful technique, but it is just harder to learn.