I think the Issue of Regency would be easier when Charles could be named Regent for a fe dayslike it is done in Norway and Denmark when the Moanrch there is ill like in Norway or absent like in Denmark.
Then Charles could be named Regent for replacing HM at for example the State Opening of Parliament and after it it is ended.
There is no need to name anyone to be Regent for a single event.
Under the law of the UK a Regency can only be established for one of two reasons:
a) the monarch is under 18
b) the monarch is TOTALLY incapacitated.
There is NO duty that The Queen has to do. Even approving legislation can be done by Counsellors of State as has happened in the past.
What does she do constitutionally?
1. Reads the boxes - the same boxes that both Charles and William now receive and even then they only have in them what the government decides to let them have e.g. in 1936 the government deliberately left documents out due to not trusting Edward VIII - is that the case now? We of course won't know for decades, and possibly centuries, if that is the case.
2. Meet with the PM once a week when Parliament is sitting - not necessary at all as there have been many weeks during her reign when parliament is sitting and she hasn't met with the PM - more a tradition than a necessity
3. Chair the Privy Council about once a month - not necessary for her to do it as it has been done by Counsellors of State many times throughout her reign
4. Open parliament - not necessary - as she hasn't done it every year during her reign. In both 1959 and 1963 it was done by the Lord Chancellor (due to the fact that she was expecting and so it wasn't done for her to be seen in public in such a state)
5. Met with incoming and outgoing High Commissioners and Ambassadors - not necessary - can be done by anyone as seen by the number of times that she passes that to someone else even now ... especially the outgoing.
When you actually look at what people say she 'has to do' and by implication only she can do as monarch there is the grand total of NOTHING that she has to do. Everything that is supposed to be her job constitutionally can be done, and has been done, during her reign by others.