Hmmmm .... "In 1998, it became an independent public organisation, wholly owned by the Treasury Solicitor on behalf of the government, with independence in setting monetary policy" ???
Absolute rubbish. I almost gave up reading the made up crap on those links but this sentence gives away what a load of crap it is "Her holding is based on the laws of the countries she owns" !!!!!!
The Queen is Head of State - she doesn't OWN countries. That would suggest she could sell them -...
I think your basing this entirely on Edwards abdication which required a specific act of parliament and the act written ONLY for his abdication.
Should the Queen ( or indeed Charles ) abdicate another, new, act of parliament will be required and it will specify the terms of that abdication...