I think switching to third person for the BAT would add a lot of tension. Whenever a series switches from first person to third person in the final book, it's a pretty solid indicator that the narrator is going to be dead by the end of the book.
The BAT is a good point to do it because the the series has constantly been pitched as 20 (now 20+) case files and then the BAT. So if the BAT isn't a case file, why would it need to be in first person?