Something I wonder is if the British monarchy could be more politically active in KR. Here is my case.
Basically the British monarchy had a lot of power in theory, but the royalty doesn't use it for stability sake. Edward VIII Otl had many outspoken opinions, and in KR he's shown as someone with autocratic tendencies.
I imagine that if Canada restore the UK with the conservatives in power and Edward VIII is the one being crowned, the British monarchy would be stronger until he dies and Elizabeth II takes power and adopt her non interventionist position from our timeline.