Okay so an update.. I've concluded that the DIR-615 is crap, and will not work for native IPv6.
I ended up getting a DIR-655, which some other users have had. I've configured it exactly as they have, and the router is able to get an IPv6 connection going, as I can ping 2001:4860:4860::8888 for example (from the router), and my computer is assigned an IPv6 address, but the 'router' address on my computer is blank, and it's not able to access anything. Almost like the router isn't pushing a route.
Here is the setup I did: