Ultimately, I believe that Canada and Denmark should share sovereignty over this island. This is, of course, a difficult solution to implement, but it is also difficult to see how the dispute can otherwise be resolved.
There is no clear-cut international law that can determine who should controls the island. Therefore, there can be no real hope for a third party ruling that will objectively determine who should own the island. This means that Denmark and Canada must compromise on a solution that would be mutually acceptable.
One possible solution might be to give Canada day-to-day control of the island since it is so much closer to Canada than to mainland Denmark. In return, perhaps Denmark should be given some portion of any revenues that come from oil under the seabed.