…whilst I disagree that we should have a foreigner as our own head of state…
The position of head of state is a matter of opinion. The Governor-General says he is, and the King doesn't.
It's not actually defined anywhere in any Australian law. I take Charles de Gaulle's position that the President of France should embody a certain idea of France as French head of state, and translating that to Australia, Charles III cannot possibly present himself as embodying any notion of Australia.
In reality, "head of state" is a diplomatic term rather than anything defined in law.
Australian Governors-General have been making head of state visits overseas since Whitlam's time. Diplomatic credentials have been addressed to the Governor-General in his own right for many years. The UN diplomatically lists both monarch and GG in their "
Blue Book"
Referendum or not, we've been walking steadily further away from Buckingham Palace since Federation. Every now and then the High Court takes another formal step on the path and we don't need to change the wording of the Constitution because it has been reinterpreted.
For example, we are now an independent nation because the High Court decided this when asked if Heather Hill, a dual Australian and British citizen, was eligible to take her Senate seat. Not a word in the Constitution was changed but although we had British - and Canadian and New Zealand - MPs in our early days, they have to renounce all other allegiances now.
I think as time goes by more and more Australians will accept that the Australian Governor-General is doing a fine job as Australian head of state. And the "King of Australia" isn't.