Excellent! I have an odd feeling I should have asked you from the start, ha!
I grew up in Alaska and while I was fairly confident most of the state was devoid of rabbits, there’s always that niggling question, “But what about the Panhandle? Who knows what strange southern flora and fauna it’s got?” Juneau for sure is host to a colony of feral European domestics.
Probably a big reason it took me as long as it did to start googling in the first place. But I just ran a search now with your info in mind, and still didn’t turn up any references to cottontails in the state.
I’m extremely appreciative of the effort you took to find and post the map, but sadly I think the black is just an artifact of extensive coastline with lots of tiny islands. Notice it’s the same along the northeastern coast of Canada, where I doubt cottontails would be at all happy. It does show a pocket of introduced cottontails in Oregon/Washington, however.
I’m afraid any more on this topic from me will have to wait for tomorrow! 