As already seen, the only remaining constitutional connection with the United Kingdom is through the monarch, who is the monarch not only of the UK, but also of Australia and of each of its States.

Ermmm???? By your own reference the Queen occupies a role in Australia because she is Queen of Australia as well as being Queen of the United Kingdom. It's up to the democratic choice of Australian citizens how long she remains in that role, nobody else. I doubt if many non-Australians care. As a self avowed "Englishman" it doesn't seem to be any of your business either way.

ETO