I need to make it from Victoria (BC) to... Somewhere in Nunavut in 10 days or less. Suggestions as to method?

Well the quickest way to cover all that territory is to fly and, in general you need to fly to get to move places in Nunavut as there really aren't many roads up there. As for how you'll do it on $560, I think your traveller will have to be a pilot with a buddy who lives in Whitehorse and owns a plane.