We also have national and provincial parks, Crown land is different. A national park is maintained for visitors and for nature, crown land is closer to unused or unclaimed land, generally nothing is done with it unless it's sold off. You are free to camp on crown land, but it's nothing like going to a park, it's full on wilderness camping with no amenities, sites, or anything else.
My point is, Canadians think of government land philosophically as something that is not theirs, but rather, owned by the crown -- the Queen. While Americans see public land as their shared land. This mentality penetrates into many of the differences between the two countries in how they govern.
"Crown" (or "Royal", "Regina", etc.) is used pretty extensively in the Canadian governmental or legal system, and any association in Canadian's minds with the Monarch are pretty much nil.
If you talked about "crown corporations", or "Regina vs." (for criminal cases) no one would associate that with Elizabeth II. "Crown" and anything like that basically just means government.
No, Canadians do not see Crown Land as owned by the Canadian Monarchy, they see Crown Land and owned and controlled by the government as a public asset.
Canadians see the Canadian Royal Family as nothing more than a figurehead of the state.
I am a Canadian and I have studied British and North American History extensively.
I somewhat agree with your main point, but I don't think most Canadians associate the "Crown" as in Crown Land or Crown Corporations with the literal monarchy. Rather it's just a synonym for the (Canadian Federal) government. Most Canadians don't tend to think about the monarchy much at all. (Certainly the Canadian Governor General, theoretically the Queen's representative as head of state, would never be expected to actually take instruction from the Queen.)