But (note, UK person here, add salt accordingly) it seems like you could retain that part while also stripping any actual power - i.e. 'power-wise practically a republic, emphasis on the -nominal- in my first sentence.'
Implementation details thereof I don't have a strong opinion on except perhaps "if I ever do develop such an opinion you should probably ignore it anyway."
I always vote "below the line" - it's more fun trying to rank all those micro-parties in order of how much I agree with them :)
It's still miles better than the UK's system
If Malayans wouldn't be so iddle Australia would be like Indonesia or rather Madagascar now and nobody would ever hear about any other natives there, like we don't hear about modern Ainu. Oldest doesn't mean better nor in any way more civilized. Australians could spend more time defending their guaranteed basic civil rights that become only theoretical in time of barbarian madness of sanitarism*. If they feel bad for aboriginal folk they can carve them big piece of Austrialia back and we will see how civilized they are at giverning themselves. But we all know Australia is equally imperial, predatory & hypocritical state as old Britain after what happened to Timor. So it won't ever happen.
In the UK, the monarchy fits pretty well with the other European constitutional monarchies, and there are reasons to support it as you say. I still think hard questions need to be asked about the exact nature of the monarchy, but it's clearly an English/Scottish/Welsh institution that belongs here.
In Australia, it's a remnant of colonialism, a foreign invader that destroyed one of the oldest, if not the oldest, civilisations on the planet. If we're ever going to get over this, then we need to remove these remnants. Having a British constitutional monarchy in modern Australia is a ridiculous anachronism. The "advantages" could clearly be replicated without the historical baggage. We need to be a republic.