You're not likely to find a remotely reasonable hypothesis, even in the Methodsverse where magic abounds, by which the internal parts of a thinking computation can be damaged by damaging the brain, and yet removing the whole brain leaves the soul capable of internal thinking.
Why not? Letting a brain decompose kills the "thinking computation", while cryonizing it supposedly does not.
Similarly, damaging a living brain may damage the attached soul, while death of a reasonably intact brain could be interpreted as a detachment of a reasonably intact soul.
Taboo death
No plot spoilers here, just wanted to flag a bit of poor reasoning that shows up in Chapter 39:
This is a surprisingly common fallacy. Just because X depends on Y, it doesn't follow that X depends on nothing but Y. A phenomenon may involve more than just its most obvious failure point.
To illustrate: Suppose I'm trapped in a box, and my only way to communicate with the outside world is via radio communication. Someone on the other end argues that I don't really exist -- "There's no person beyond the radio receiver, for if there was then there wouldn't be any such thing as damaged radios!" Pretty silly, huh? But people say this kind of thing in defense of physicalism all the time.
(N.B. This is not to defend the existence of souls. It's just to point out that this particular argument against them is invalid.)