What would have to happen for an upcoming British monarch to not be of House (Mountbatten-) Windsor?

No, we rejected the presented republican model, and the alternatives because we couldn’t agree what powers the President should have vis-à-vis the Prime Minister. A rather more important question.

That model, known as the McGarvie model, was presented as a viable option and had some, but insufficient support. Indeed I am a card carrying member.

No. Australians wanted a less Presidential model. And in the aftermath of the republican high water mark, which was way back in 1999, the ARM movement is currently moribund and couldn’t win a chook raffle.

For those wanting the indulgence, my previous post on the Australian Constitutional Convention, 1998 and subsequent lost referendum.