My guess is that the blank space indicates the grave was set up by Kōtarō, and he is the surviving son (having buried his parents and brothers). Since he expects to be interred there too, he has already carved his name on the stone as a sort of declaration (which isn't uncommon). The wife Setsu is somewhat ambiguous. We don't know whose wife she is: is she the wife of Kōtarō, or is she the wife of the Tsunejiro, whom she is buried next to? (A minor diversion.)
There is no other marking, except for the face of the stone which reads 中村家之墓 (Nakamura-ke No Haka). The oldest date on there is Meiji 30 (1897) which is well after the dissolution of the class system.
The confusion over Tsunejiro/Tsunetaro is doing my head in. The possibility you allude to in your post #29 above (that there may indeed be both a Tsunetaro as well as a Tsunejiro) cannot be denied. But it does seem highly unlikely. Let's leave this aside for now until/unless you have some other interesting info on this.
My guess is that the clothes are still too casual for a one-year memorial (一周忌). In Tokyo, a family of means would have had a proper, formal one-year memorial, and would have worn black for this. Nowadays things are much more casual. Hiroshima customs may allow for different levels of formality.
it is a great dishonor to exaggerate or misrepresent your status
It wouldn't be any sort of dishonor whatsoever for a farming family of means, or a wealthy merchant family to be ostentatious in clothes or houses or gravesites or any of this stuff. It wouldn't have been at all out of character or illegal or improper for them to adopt the fashions of the elite classes. Actually it would be been completely in character and practically
expected of them to do this. Status is fluid, as I mentioned before. And I think you can say for sure that the family had money, (proper, large gravesite/tomb, proper kimonos for the ladies, proper suits and kimonos for the men). I'm already intrigued by the Nakamura family as it is. Whether they came from bushi, or if they were very clever with their money... to me its just different flavors of cake.