My question. Can the parliament not just pick someone one else to be King/Queen or is it the House of Windsor?
This here is where a lot of people get mixed up with the whole Monarchy debate.
Monarchs are given their "power" (even symbolically) from the concept of
"The Divine Right of Kings" . The House of Windsor maintains the right to rule based off it being the will of God. Del Gratia Regina "By the Grace of God" is more than just something we stamp on coins for the hell of it.
Parliament derives it's authority from the people to represent them, however, it derives its power from the Crown. The Crown being more than the person that wears it, but more the concept that it's willed by God through the monarch.
It gets messy trying to modernize and deomcratize something that is very much not a democratic institution. There is a reason the Declaration of Independence added the "all men are created equal" part; it prevents any one person to claim divine right within a republican ideal.
The issue arises in a Republic when you do get a tyrant (45) into a position of absolute power, however, the checks and balances in place fail spectacularly ( Impeachment, Senate Trial, etc.). In essence, we retain the monarchy as it is as a kind of... i don't know.. .compromise? to both ideals.
My point is to not open the constitution and everything that goes with. Keep all the offices just "Canadianize" the top one some way.
We Canadianize the office by having Canadian citizens appointed as the Vice Regal. That in and of itself is an anomaly and broke the mold of the position of Vice Regal. The concept of the Vice Regal was someone, usually a peer or a member of the Royal Family, was to serve in this position so that loyalty to the Crown was guaranteed. When Vincent Massey was appointed in 1952, it was the first time a Canadian citizen, without peer or title, took on the full powers of the Monarch within Canada. This became the status quo and will stay as such, lest we do something crazy and become a republic.