“The problem is that you’d have to go above the arctic circle before you get somewhere with less than a 6-hour day on December 21st.”
Not true. I went to myzmanim.com and looked up Trondheim, Norway, for 12/21/2014. (Trondheim has the northernmost orthodox synagogue in the world, but it is still south of the Arctic Circle.) Sunrise is 10:01am and Sunset is 2:32pm.
(Tomorrow night, candlelighting is at 10:56pm, and Shabat does not end because it won’t get dark enough to see three stars. In fact, it has not been dark enough there to see three stars for weeks. )