Elizabeth, Queen of independent Scotland?

In a week from today, the Scots will vote over whether Scotland should become an independent country. While the no campaign has had a clear lead for months, the opinion polls are now so close that the dissolution of the United Kingdom of Great Britain and Northern Ireland is a real possibility. If a majority of the Scots votes yes, Scotland will become independent on 24 March 2016. If they vote no, we have now been told that Scotland will immediately be offered greater autonomy within the United Kingdom.
A yes vote will obviously have great consequences, so it is rather surprising that many crucial issues remain unclear, most significantly the financial issue. While the Scottish government insists that Scotland will maintain the pound as its currency, the leaders of the three main British parties have insisted Scotland will not be allowed to do so, and should they change their mind a currency union between Scotland and Britain would clearly involve some sovereignty being ceded. It is also quite surprising that the British government insist they have no plans for what will happen if Scotland votes yes.
The question of what will happen to the monarchy has on the other hand been settled, although it includes unanswered questions. The referendum is about the dissolution of the parliamentary union of 1707, not the union of crowns of 1603. Therefore a vote in favour of independence means that Scotland and the remainder of Britain will revert to the previous arrangement, i.e. a personal union between two independent states. This is roughly the same arrangement as the union between Britain and Hanover between 1714 and 1837 and the union between Norway and Sweden between 1814 and 1905.
This means that Elizabeth II will become Queen of Scotland or of Scots, the latter (and, I believe, older) title apparently being favoured by the Scots. She will obviously drop the numeral in Scotland, as she is the first Scottish monarch of that name. This will put Scotland in the same position as Australia, Canada and numerous other kingdoms of which Elizabeth II is queen, i.e. of having a monarch resident abroad, although I can imagine the Scots will expect her to come to Scotland more frequently. As Queen of an independent Scotland Queen Elizabeth would be bound to take constitutional advice from the Scottish government, which may mean that she could at some stage receive conflicting advice from the Scottish and British governments in her roles as head of state of both countries (the union kings of Norway and of Sweden would have had much to say about such a scenario). One possibility is that her functions as Queen of Scotland is delegated to a governor general or a similar office when she is not in residence in Scotland, as is the case in her other kingdoms, but this has not been officially discussed.
There is also the issue of how long such a personal union would last. A YouGov poll conducted on 2-5 September found 54 % to be in favour of keeping the British monarch as head of state in the event of independence, while 31 % favoured an elected head of state and 15 % were undecided.
The same opinion poll found, for the first time, a majority to be in favour of independence, which has unleashed what seems like panic in London and some rather desperate calls for Queen Elizabeth to intervene and speak out in favour of the union. At the time of her silver jubilee in 1977, when a referendum on devolution of powers within the United Kingdom was coming up, the Queen for once indicated her personal opinion in an address to the Houses of Parliament, saying: "I number Kings and Queens of England and of Scotland, and Princes of Wales among my ancestors and so I can readily understand these aspirations. But I cannot forget that I was crowned Queen of the United Kingdom of Great Britain and Northern Ireland. Perhaps this Jubilee is a time to remind ourselves of the benefits which union has conferred, at home and in our international dealings, on the inhabitants of all parts of this United Kingdom".
On Tuesday the conservative Daily Telegraph used its editorial to call on Queen Elizabeth to speak out in favour of the union. This was rejected outright by a spokesperson who insisted: "The sovereign's constitutional impartiality is an established principle of our democracy and one which the Queen has demonstrated throughout her reign. As such the monarch is above politics and those in political office have a duty to ensure that this remains the case. Any suggestion that the Queen would wish to influence the outcome of the current referendum campaign is categorically wrong. Her Majesty is firmly of the view that this is a matter for the people of Scotland". It would in my opinion have been unwise if she had indeed intervened. It would have jeopardised the monarchy's political neutrality, and might also have alienated it from roughly half the Scottish people. It would also have undermined the Queen's standing, as it would have made a yes vote a personal defeat for Elizabeth II.