Ah this "elusive" set of "real" Canadian values and indentity. I have always found it puzzling (from afar) why Canadians are continuously looking for something that is right under their noses. I have a theory, bare with me on this.
Let's begin with your history and the myths extracted from it (all socieites have it, I'm not knocking Canadians). On July 1st 1867, The Dominion of Canada came to be, a carving of political boundaries affirming Canada's allegiance to the British Crown. A hundred years later and them some, Dominion Day was renamed Canada Day (first mistake from my point of view). All you did was change the name, not the meaning of it. You continue to celebrate "Canada Day" as your country's birth, but in reality, you are celebrating the country's allegiance to a monarch thousands of miles away. What you should be celebrating (again in my view) is December 11th 1931 (date?) when the Statute of Westminster came to be.
If there is any single defining moment in Canadian history (as difficult as it may be considering Canada evolved into indepedence) it would be that date in which Canada begins to detach itself from the British Empire. If you don't believe me, ask Canadians (I have) what Canada Day represents, and in most cases you will get a different answer. Some will tell you it was merely a tactic of compromise and consent to delay independence for another 100 years. Others will tell you its the day Canada was "born" etc... The bottom line is everybody has a different understanding of it. Even historians (Canadian) are hard pressed to find the definitive moment when the British Empire ceased to exert influence and the Canadian indentity emerged.
Another issue (again in my opinion) is the attachment many in Canada have to the monarchy. The monarchy is part of Canada's history, yes I agree, history as I mentioned is an integral part of a country's indentity. That doesn't mean you have to hang on to it, you have to look forward, not dwell on the past. I have often heard the argument of swapping the monarchy with a President like GWB. My answer is, there in lies another key problem. Canadians are stuck in the past. Their options (apparently) are limited to either a monarch or a Constitutional Republic like the US. Well you don't need either, make something up that is uniquely Canadian. Perhaps a mixture of both systems?
I'm not going to continue blabbing, but in short, your institutions are fundamentally British and your day to day lives are fundamentally similar to Americans. But that in itself is not a problem, the problem is you are stuck between a rock and a hard place. You just won't let go of the past. Cherish and know your history and be proud of it, you don't have to hang on to it.
All these little and subtle nuances is what makes an indentity. The US war born of blood and battle, Canada was born through compromise and consent. You have to tweak the defining moment when Canada came to be, because you were part of the New World. You weren't hanging around Canada for thousands of years like the Greeks, Italians the French and so forth. So you need your "moment in time".
In conclusion, my view of the Canadian "indentity" is that you are a new country struggling to define itself. It took the US clear over a century to do so. You're not out the woods yet. And if I may be so bold, stop being obsessed with what the world thinks about you, just be yourselves, the world doesn't give a phuck about anybody except themselves.
