No plot spoilers here, just wanted to flag a bit of poor reasoning that shows up in Chapter 39:
I shouldn't have believed it even for all of thirty seconds! Because if people had souls there wouldn't be any such thing as brain damage, if your soul could go on speaking after your whole brain was gone, how could damage to the left cerebral hemisphere take away your ability to talk?
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.)
It is similar to the Witnesses as far as your description goes, though I am not very familiar with JW's beliefs to comment further on the similarities.
My only point was that this is an old idea (that you need a body to function and that you get given a new body of some wondrous sort upon death), and not one contrived as an escape from the physicalists death blow. The debate is over and done for me, and I as you see the moves of the dualist as always failing to substantiate the additional substance.