I see you've got your choices pretty settled, but I'll add my thoughts for anyone else following along and thinking along the same lines.
I'd be leaning towards a lighter folder. Since the BK2 will handle the bigger tasks. I've not spent much time at all in the BC old-growth, but from what I do know, chopping and battening will be much more limited to pretty small stuff anyway, and its not like you will be building a house with just the BK2. I like the idea of a solid leatherman, like the Wave or 300 for any time I'm doing anything sort of semi-urban building/work/fun. That will likely see more use than a dedicated folder, at least on the job-site (swisstool is also a great choice). I'd go for a folder that also can handle your food prep/fishing/ or a smaller fixed for that purpose (easier to clean).
As for BK2 vs. hatchet, personal taste. I don't think either will really have a solid advantage where you are going, personal technique will make a bigger difference than the tool.
As much as its kinda a dumb idea, as in not terribly practical, summer in bear country, a fixed blade will be a better idea than almost anything else if it comes to that. So the BK still has a place I think. But to each their own.