You can keep your 'king'
I don't particularly want him or know anyone who does - I'm not hugely bothered by coronation or it's costs as I suspect soft power wise and politically we'll manged to make it work for us and it is our current system.
I'm also not really pro monarchy - I just not keen on presidential replacement system though it politicians put the effort in I could probably get sold on it.
did Philip say they'd 'go quietly'
I suspect King Charles would hang on to the bitter end though I have less Idea about William.
Prince Philip own background of being member of displaced monarchy would be playing into that - his own descendent may well have a very different view based on their experiences and he now longer here to influence them.
I don;t more in political Republican circles and I'm not seeing what you are describing - though with Queen gone I'd not be surprised if they made more effort as monarchy is most vulnerable for decades - I'm not sure it will have a huge impact yet though.
They will start by reforming the House of Lords
-Removing the COE bishops or including other religions
There's many more than ardent republican wanting this - and it's not happened yet or clear it will any time soon.
I really hope it doesn't get seen as a republican stance or first step and drive away more nuance support - as frankly it need to happen and needs widespread support to do so.