Jeez, this subject's like a vampire. Every time I start thinking it's dead, somebody pulls the stake out of its heart.I feel that serious changes should be made to the constitution to change Canada into a Federal Presidential Republic.
A republic is simply a form of government in which the head of state is elected in some fashion rather than being related to a hereditary monarchy. All Canada need do to become a republic is make the Governor-General an elected position. We wouldn't even have to change the job title. All references to the Crown and the monarch in statutes, regulations, and titles, would have to be altered--no more Court of Queen's Bench, for instance--but those are fairly trivial and don't require any substantive change. Becoming a republic would not in itself necessarily have any positive effect on any of the problems you mention, and might make some of them worse. The President or Governor or Archon or Doge or whatever we choose to name the job, as an elected official can be expected to be partisan. Any incumbent will feel a certain political legitimacy that is not currently associated with the position, and thus entitled to speak out on matters of public policy.
From what you've posted so far, you don't appear to know enough about this to think clearly about it. Regional interests would remain as they are, the structure and functions of parliaments and legislatures could remain as they are, the powers of the two orders of government could remain as they are, the concentration of power in the PMO could remain as it is, the electoral system could remain as it is... Becoming a republic wouldn't in itself require any change in those areas. It's not a solution to anything important and seems likely to just create more issues.