I think that the last Case File before the BAT will end with Harry pretty much retiring. Personally, my bet is that Murphy dies in the last book, and it's the final straw for Dresden. He's going to hang up his nonexistent hat when she bites it, and will retreat to live out his days on Demonreach.
Then the Apocalypses (I'm assuming that the BAT will involve lots of Apocalypse stories, from the Abrahamic Religions, Ragnarok (naturally), the Shakers' Apocalypse (overdue by a couple of centuries; I think there are actually a few Shakers left, believe it or not, since celibacy is a requirement. Pretty sure there are a few dozen living in the last Shaker community up in Maine), etc.) kick off, and Harry returns from his period of mourning and hermitude to kick back.
I'm anticipating a barely-in-control Harry during the BAT, similar to his breakneck pace and recklessness in Changes. Though I anticipate a different ending.
Personally, I don't think the BAT will end with Harry's death, per se. I think it'll end with Harry Becoming Something Else. A guardian deity-type figure, with a bit of Trickster thrown in. Though that's tied into what I think he'll do with the Winter Knight's Mantle after Winter loses the Gates and the Fae Courts are pretty much gone.
Part of my BAT WAG is that it'll be written from multiple first-person perspectives, shifting around between Molly, Dresden, maybe Maggie, and other Important Players. Since the Case Files are, per Jim, "written" by Harry (the way he puts it, they're Harry "looking back" over his life), I think the BAT is going to be different. We know Harry lives up to the BAT because he has to write this stuff down, right? Or, at least, share it with someone else. I think that'll happen between the end of the Case Files and the BAT.
Changing the format of the BAT is one way to make it clear that Harry might not make it out of things alive. It can also be a good way to accurately communicate and explore the scope of a truly apocalyptic conflict, grander in scale than even First Lord's Fury.
I don't want Dresden to ever end, but I do want to know what happens.