Hones hard and medium hard, just my opinion
The barber hones that I have seen with the Nakayama stamps on them are usually very hard and gray. I believe that Kato-san the owner of the Nakayama mine worked with Iwasaki-san the Sanjo blacksmith who is famous for his kamisor razors to create a "class" of razor hones with certain specific characteristics so that they would work well with Aichi/Mikawa nagura.
This was a designed formula system from the 1950s that used hard base stones and soft nagura. The important ingredient was the nagura, and the nagura had to be of the highest quality. Without the nagura the system could not be used because the stones were too hard to use alone. This system was designed for all barbers in Japan so that high quality standards could be followed. Iwasaki also encouraged barbers to have a microscope in their shop to use to check their razors.
The idea of high quality stones that were super hard was a boom for Kato-san because until then very hard stones were impossible to use and not easy to sell. Barbers did use tomonagura with hard stones but from what I have seen myself when visiting old barber shops in Japan, I saw mostly medium soft to medium hard stones were being used.
Of course all of this took place way before a diamond plate had been invented. Now with the Mikawa nagura mines closed, and nagura getting very expensive some people with super hard level 5+++ stones are using diamond plates to raise a slurry.
Kato-san did not ink stamp very many of his stones, but him main wholesaler Hatanaka-san did stamp the stones he sold wholesale, and these are what we usually see as or know of as Nakayama stamped stones. Kato-san was not a retailer so ink stamping stone except for his famous Maruka stamp are somewhat difficult to recognize.
About more expensive and ink stamped Nakayama stones. Ink stamps add more value to a stone at the retail level, but they do not make the stone better. You have to try out the stones to determine how good it is. If you are going to buy a stamped Nakayama stone, try to buy one from a seller who will give you a money back guarantee.
At the ultra high or fine grit levels of razor hones, stamped or not stamped, the difference in the actual grit from stone to stone or mine to mine is not all that different, sort of like the difference between 15,000 and 17,000 as an example. Both will hone a razor or should be able to give a great edge. The difference and the real greatness in Jnats from stone to stone or mine to mine in my opinion is the character of the stones and how easy they are to use and how different the binders or clays can be. This is why I am not a big fan of L5+++ stones. They only do one thing, polish.
There is a whole world out there of L5+, L5, L5-, L4+ stones that are easy to use and will make a razor just as sharp. These medium hard stones have many chapters, like in a book, each chapter provides opportunities to learn from and to hone different types of steels. Level 5+++ stones (in my opinion) only have one chapter.
I welcome any comment.
Happy Honing, Alx