Pretty sure you are correct about the only Australian based
organisation, but I think the difference is that Aikikai Australia is affiliated directly to the Honbu, where other organizations such as AKI and AAA are affiliated to the honbu via overseas aikikai shihan (ie. Japan (Tekada Shihan) and USA (Nadeau Shihan) for these 2 examples) and can still award Aikikai Dan rankings.
It is interesting that I have trained with at least 2 senior Aikidoka in US who were very surprised that I was not from Aikikai Aust because when they visited Australia with Yamada sensei, they were told by the locals that Aikikai was the only Aikido organisation in the country. May be a language barrier with the Americans and Australian, I find that a lot here
I think Aikido landscape and history in Australia is quite devise and I would be very interested in what the original poster could put together.