On the "old" Japanese forum however, I found her obituary that apparently gives the birthdate of 18 August instead (which, when adapted to Gregorian calendar, apparently gives the birthdate of 16 September 1856).

The Japanese Data Website also gives 16 September 1856 as a possible birth date, see here.

On the "old" Japanese forum

I don't know about Mrs. Yoshigiku Ito but above "old" is not a forum site, technically. It called anonymous chat-like site, 2 channel. https://en.wikipedia.org/wiki/2channel

By 2016 2 channel was full of troll and spam post, that's why people needs and move to a new place...

The GRG (more precisely GWR) validated her with the birthdate of 3 August 1856, and Japanese Wikipedia also uses that date ("1856年8月3日（安政3年7月3日）" - they even added Ansei period birthdate). However, Data Collection Site and the Japanese forum are using 1 September 1856 as her birthdate, and I have not seen an explanation for where this date came from. Japan was not using the Gregorian calendar when she was born, so I suppose the GWR validated her without properly adapting her birthdate to the new calendar, and the 1 September birthdate would be the correct one? 

On the "old" Japanese forum however, I found her obituary that apparently gives the birthdate of 18 August instead (which, when adapted to Gregorian calendar, apparently gives the birthdate of 16 September 1856).

So which one is the correct one?