If Greenland's mile-thick continental ice disappears to reveal the geology beneath, I don't think there will be any human civilization still around able to exploit it.

Not only will the sea level rise (from melting Greenland ice alone) devastate the world's coastal populations, the amount of heat required to melt that thick glacier will be destructive to the rest of the planet. In fact, in the worst case scenarios, the highlands of Greenland and Antarctica may become the last redoubts of humanity, with the remnants of our species huddled at and clinging to, and following the edges of a rapidly retreating glacier.

No, I don't think the worst case scenario will materialize. Long before that point comes, human industrial civilization, the cause of this catastrophe, will have disappeared. In a few centuries, the warming will stop, the global climate will stabilize, and we will be a hunter gather society again. If we are lucky enough to survive at all. In a thousand years, barely a trace of our civilization will survive.

But it will make an interesting sci-fi scenario: A bi-polar world, with the few remaining human survivors living at either pole, isolated from each other, with a hot and uninhabitable equatorial belt separating them for eternity.

The polar projection map illustrates nicely the geographical significance of the Arctic Ocean, a new Mare Nostrum, not unlike the Bronze Age Mediterranean. All the world's land masses surrounding it, and all the ocean highways from the rest of the world leading away, and converging there. Your other map, showing contemporary claims, illustrates what will have to be resolved politically--or militarily, before that world can be.