If someone already mentioned this and I missed it (I did look) I apologize.
One of the most significant manifestations of our lack of control over the Arctic is the presence of US, Russian, and other nuclear submarines under the icecap. These will be next to impossible to control with icebreakers anyway, and I doubt satellites can help (don't have a shooter capability, after all).
The only real solution is a nuclear submarine, like the Mulroney gov't recognized in the 80's. The problem's still the same, isn't it (except for the Soviet threat)? If we had just two, that would probably be enough to provide an effective demonstration of sovereignty - AND a way to enforce it (which, as stated above, icebreakers, sats can't do).
I know the US wouldn't look highly on us developing that capability - they didn't in the 80's. Maybe the French could help. They've got a 2600-ton displacement nuclear class called the Rubis...
Maybe one of our resident Navy guys could comment.