This is a topic that shouldn't be allowed as the syllabus clearly says that you can't 'significantly overlap any SC or HSC examinable syllabus' and Hirohito is one of the personalities on the Modern History syllabus. The actual wording from the Extension History syllabus is:
must not overlap significantly with the examinable content of any other School
Certificate or Higher School Certificate course.
My Head of Dept actually rang the BOS to get a ruling on a question one of my students wanted to do that related to a topic that we don't teach but is also on the syllabus and we were told in no uncertain terms that it was a definite NO.
If your school allows you to do it then fine but they are going against the syllabus of the course.
No - it is any examinable syllabus not just ones you are studying or even subjects taught at your school. The syllabus clearly says 'must not overlap significantly with the examinable content of any other School Certificate or Higher School Certificate course.'
Ask yourself - does doing a research project on Hirohito 'significantly overlap with the examinable content of the HSC Modern History course where Hirohito is an option' and your answer is "Yes" so you can't do Hirohito for your project.
What your school is allowing you to do is unethical at least - sorry - but they are giving you an unfair advantage as you could decide to do the Hirohito question in the exam rather than Ho.
It is for reasons like this that I would love to see the projects externally marked so that teachers aren't allowing their students to not abide by the syllabus set by the BOS.
Good luck to you that you have a school not following the rules.
If you think about it - why did it state 'School Certificate syllabus' when obviously students wouldn't be studying that content for the HSC?