These are interesting points that have been touched on before but it isn't strictly speaking a shared monarchy. It's a shared monarch. For the moment at least.
The realms are in a probably transitory personal union. They don't have to have the same line of succession any more than the UK & Hannover did.
Even assuming it would be possible to do it, it would be a huge mistake for the UK to change the line of succession unilaterally bypassing the Commonwealth Realms. In fact that would be a huge boost to the republicans in those countries.
As another Canadian, I am not sure our current government would even want to be involved. Isn't there a way of kicking the can back, similarly to how I believe the succession law here was tied back to the UK?
Not an expert here, but, as far as I understand, what the Canadian courts said is that:
1. The rules of succession are not part of Canadian law or the Canadian constitution.
2. The principle of symmetry in the preamble to the Constitution Act, 1867 implies that the person who occupies the throne of the United Kingdom under the British laws of succession is automatically the King or Queen of Canada.
3. It follows from (1) and (2) that no change to Canadian law or the Canadian constitution is necessary to change the rules of succession.
However, under the preamble to the Statute of Westminster, 1931, which is
still in force in Canada and is part of Canadian law, the Parliament of Canada is required to assent to any act of the UK Parliament changing the law of succession. That is why the Parliament of Canada had to pass the
Succession to the Throne Act, 2013 . Note that the text of the linked Canadian act does not change any point in Canadian law, but rather merely assents to the British Succession to the Crown Act.
BTW, the Supreme Court of Canada refused in 2020 leave to appeal against the ruling above of Court of Appeal of Quebec, so that interpretation, as weird as it is, is now the law of the land in Canada.
It is weird because, in 1936, in addition to an
act of the Canadian Parliament merely
assenting to the UK Parliament's Abdication Act under the preamble to the Statute of Westminster, the government of Canada also issued an
Order in Council consenting to the same act under S.4 of the Statute of Westminster (now repealed in Canada), which dealt specifically with incorporation of acts of the British Parliament into Canadian law. The plaintiffs used that latter fact as evidence that the law of succession was indeed part of Canadian law, but the Court of Appeal rejected that opinion in a somewhat convoluted ruling where it argued that the Abdication Act was different in nature from the Succession to the Crown Act because it not only changed the order of succession and the rules for disqualification, but also affected the principle of hereditary succession which, according to the Court,
is part of the Canadian constitution.
Australia, on the other hand, took a
diametrically opposed position and asserted that the law of succession is not only part of Australian federal law, but also actually part of the law of each individual Australian state,. Since S.4 of the Statute of Westminster was repealed in Australia by the Australia Act, 1986 and no act of the UK Parliament can now extend to Australia , there was no alternative but to amend both federal and state law, which is partly why it took two years for Australia to ratify the Succession to the Crown Act.