I hunted caribou in Greenland 3 years ago. I found the booking site on BOOK YOUR HUNT.com Click on Caribou, and you will find lots of very expensive hunts in Canada and Alaska, but one pops up in the 5K + range. I could have shot a musk ox also if I wanted to pay for it, and did have a couple opportunities. I did write an extensive review for the site titled, "Mission Accomplished" if you can find it.
The outfitter is based out of Kangerlussarq, and travel there is the biggest hassle. A new airport in the capital of Nuuk has changed the route, and not necessarily for the better. It was 4K when I went, but as in all things the rates have gone up, and he is booked for the next two years. You can call me at #218-834-3646. Rick