My name is Casper, I'm new here. I'm a neuroscientist and an astrophysicist, at the same time :). I'll try to keep it short because there's so much to say on this topic. (edit: Wow I sure didn't succeed in keeping it short!)
I personally find the perspective of emergentism / dynamicism to be very fruitful when thinking about the relationship between consciousness and the brain. It helps to step beyond the whole physicalism-dualism dichotomy. It can be summarized by the statement of Gestalt psychologist Kurt Koffka: "The whole is other than the sum of its parts." I always come back to that one because its implications are so profound. Taken seriously, it implies that consciousness can be something fundamentally different from the brain, yet still emergent from it. Also, consciousness as a higher order phenomenon can act indirectly on neural processes by constraining the possible outcomes.
Soul is describing something altogether different (although not separate) from consciousness. The soul is the life of a person. I think the life of a person can never be separated from the body because we need our bodies to have human life in any meaningful sense. This is also why the bodily resurrection is so crucial to the Gospel. So what happens between our death and the Second Coming? Well I suppose we sort of exit time and pass into the Kingdom immediately. Jesus said to the criminal next to him on the cross, "Truly, I tell you, today you will be with me in Paradise."
I don't know whether Sarah Lane Ritchie is still following this thread, but I would like to respond to something she said in her first post here:
I find nonreductive physicalism to be unsatisfying instance of wanting to "have one's cake and eat it too." That is, nonreductive physicalists want the credibility that often comes with calling yourself a physicalist - it's an academically respectable position.
I think this is not a fair accusation to make if the science is strongly indicating a physical origin of consciousness (which is indeed the case if you ask any neuroscientist...). Compare this situation to that of an astronomer who wants to integrate the old age of the universe with his or her faith. Is this motivated by a desire to be respected by one's colleagues? Surely not. It is a commitment to truth that drives this. Or the same could be said of a geneticist who is grappling with the idea of a historical Adam as the sole progenitor of the human race. Indeed, the same accusation is often made by Ken Ham and colleagues towards Christian scientists who accept the evidence for evolution, "They just do that because they want to fit in with their secular colleagues." With the cake reference you even compare it to an act of indulgence. This is simply not a helpful accusation if we're looking for constructive dialogue. Naturally, every scientist tries to integrate familiar scientific knowledge with one's overall worldview. I think we should be looking beyond such taunts to be able to understand each other.
Blessings,
Casper