I know there's some point where there is no more public access, but I'm not sure if that station is part of the restrictions or not. If you want to get all the way to the Arctic Ocean, you have to arrange it with some tour companies (although it's pretty trivial to do). Generally a solo drive will consist of taking AK-11 to its actual northern end (very close to that spot), and then you can keep going to some small little motels in the area.
I've yet to do the whole thing solo but my goal is to finally do it next winter. (Been as far as the Arctic Circle sign). I was surprised at how easy the drive was, it wasn't at all the horribly dangerous drive that I was led to believe. (Frankly, other highways such as Steese were in much worse shape). Even in winter, was a pretty simple drive, the main rule being you just yield to any trucks that pass by. So I'm excited at the idea of finally getting the whole thing clinched. Been very interested in cresting the Brooks Range.