Yes, I agree the Hazuy and Hadori stones are uchigumori, but they have different purpose, the hadori is most finest, smallest and does not have any sharp angles. So they are prepared different, so you will have different results otherwise they will not have the step by step technique. So this will effect the hamon and the habuchi, like said before the polishers wants to bring out the hamon clearly. The effect on the jizuya stone, it turns out to be more white, right? You also have some different hardness between “in” the stones, so this will affect also.
I am not pretty sure how the tanpan polishing will effect the area from shinogi to hasaki if you use it with lower ratio, it will effect the hamon with colors like I told you. But it is speculaiton because I have not been there. The tanpan technique is basicly something more for the Ji-hada but used on the entire blade between the shinogi and ha, you will have colors coming up, it is something I have seen at a chinese forge. Japanese polishers will probably use different techniques not all out of books, but will sometimes give it a try, I suggest.
The white Hamon is something NBTHK really want to see in my opinion, and diffent colors will not occur due to folding the steel, this really is wrong, I have seen hunderds of folded “chinese” katana’s and I have never seen this, so I am just telling from my own experience.
Ashi are really coming from the mune, so it is obious they are more softer, I do not think I have to tell you all the advantages of differential hardening. It really is softer steel embedded in harder steel, so you are really wrong about this, even the chinese forges do understand this very clear. I will look this after when I am back from my work.
I am always traveling and picking up knowledge, I do not ask anything, just giving my thoughts.