You can't have the former without the latter
I think we could. In practice they are chosen by the Prime Minister, so we could formalize this practice locally without the crown, but without resorting to an unnecessary election.
Why not have the Prime Minister appoint the President, who must be confirmed by parliament, and keep the role of the President to be mostly ceremonial. Not much changes from today except the removal of the Crown.
The oath of allegiance can be changed to that of a republic which represents all humans in Canada.
Yes absolutely, any change to the monarchy needs a constitutional amendment, which basically means “not gonna happen” because of everything you outlined, unless there’s a massive shift in opinion among Canadians.
The best short term outcome here is probably for the Canadian government and courts to just conveniently ignore or bend some rules… let these people swear an oath of allegiance to the constitution and let a judge do some hand wavy legal magic and say “hmm, close enough”.