How do people reconcile science with the idea of an afterlife?

In all of the recent brouhaha over theism, atheism, and science (especially evolution), there’s one question which I haven’t seen much discussed. Since I can’t see an obvious answer, I thought I’d blog about it.
This question is specifically addressed to those people who accept the current state of brain science, and who also themselves as Christians (or Muslims, I guess). What kind of “brain science” am I talking about? Well, check out Wikipedia on neuropsychology, specifically cognitive neuropsychology. Read about the ground-breaking Phineas Gage and HM cases. Do you find these accounts convincing? Are they consistent with the relationship between the brain – its physical structures and electrochemical operation – and human behaviour, personality, cognition, and so forth? Of course we don’t understand all of the mechanisms and relationships today, but if you believe that science is broadly “on the right track” in these areas, then I’m talking to you.
I have no idea how many people meet these two criteria, but I assume it’s quite a large number. My question for them is not about belief in god. I’ve heard so many different definitions of the term “god” from so many people that, frankly, I’m not sure that it’s particularly useful. Instead, I want to know if you believe in life after death, and if so how you imagine it. Do you believe that you continue to exist after your physical body is dead, and if so in what form? Pehaps more important, in what sense is that which survives you? Does it have your memories, your personality, your beliefs and desires?
It seems to me that this question ought to be more productive than one about god. After all, we have a rich culture of stories revolving around notions of identity, “possession”, and so forth, from Greek mythology to Kafka to Star Trek. We may disagree on the plausibility of certain stories, but we don’t have much difficulty understanding and discussing them. So even if you can’t explain what it might be that survives you, you probably have an intuitive and accessible sense of what it means for it to be you that survives.
I’m sure you can see where I’m going with this question, but let me elaborate a bit, assuming that you believe in life after death. (If you don’t, I’m curious as to how you square this with your professed religious affiliation.)
First, how do you conceive of this something that lives on? (You probably use some term like “spirit” or “soul”, but those are ambiguous and suggestive; let’s just call it WPAYPD, for what persists after your physical death). You’ll have to educate me, because I don’t have any idea what you’re talking about here. Even if you can’t explain what it is, can you at least explain in what way it is you? What characteristics does it possess? How are these characteristics of your WPAYPD related to the stuff your brain does?
[A short digression. When I say that I don’t have any idea about this, I’m talking about the explanatory step, not the intuitive one. I’m pretty sure that you and I experience first-person consciousness in very much the same way. However when I think about “what’s really going on”, I understand it purely as “natural processes happening in my physical brain”, with no supernatural stuff involved. I’m pretty sure that people who believe in life after death have a different explanation, but I have no idea what it is.]
However you conceive of the relationship between brain and WPAYPD, I assume (correct me if I’m wrong!) that you believe that this relationship ends at the moment your brain ceases to function. Does that mean that the enduring properties of WPAYPD are determined by the state of your brain at the moment of death? If so, I wonder if you could comment on this thought experiment.
Let’s consider three plausible scenarios. In one, you live a happy life and die suddenly from a massive coronary on your 40th birthday. WPAYPD continues to exist. It has certain characteristics. In the second scenario, you suffer a Gage-like acident on your 40th birthday. You live for 10 years, during which time your personality and beliefs are observed to change dramatically. You become morose and belligerent. Then you die, survived by your WPAYPD. Are these two WPAYPDs the same, or different? Why – and how? If it makes sense for your WPAYPD to have a “personality”, is it happy or morose?
In the third senario, you contract a wasting neurological condition which leads to an inexorable loss of brain function. By the time you actually die, your brain has shrivelled to almost nothing, and you are effectively a vegetable. What of your WPAYPD now?
(When I mentioned this to a friend, he said, “Oh, that’s easy. It’s the real you” But this means that the “real” you is necessarily a-temporal and non-contingent, which seems deeply impoverishing, not to mention incompatible with the variety of free will that most religions espouse.)
Most believers think of life after death, souls, spirits, etc. as stuff which is intrinsically supernatural; they’d argue that it doesn’t make sense to ask for a natural explanation of a supernatural phenomenon. That’s why discussions of god between theists and atheists are often so unproductive. However, in this case the believer in life after death is talking about supernatural concepts that are intimately related to our intuitive notion of “self”, as well as our scientific understanding of mind, brain, and behaviour. So how do you think (or feel) about the relationship between the natural and supernatural, as it applies to the idea of life after death? Compartmentalization? A “mystery”? Predestination? And do you appreciate why I’m puzzled about how you deal with it?