I understand what you are saying, and I think that most people would agree with your analysis (at least, once it is explained to them). But I also think that it is not entirely coherent. For example, imagine that we had the technology to replace neurons with nanocircuits. We inject you with nanobots and slowly, over the course of years, each of your brain cells are replaced with electronic equivalents. This happens so slowly that you do not even notice -- conscious is maintained unbroken. Then, one at a time, the circuits and feedback loops are optimized; this you do notice, as you get a better memory and you can think faster and more clearly; throughout this, however, your consciousness is maintained unbroken. Then your memory is transcribed onto a more efficient storage medium (still connected to your brain, and with no downtime). You can see where this is going. There is no point where it is clear that one you ceases and another begins, but at the end of the process you are a 'computer body'. Moreover, while I set this up to happen over years, there's no obvious reason that you couldn't speed the example up to take seconds.

Wizard has given another example; most of us accept Star Trek style transporters as a perfectly reasonable concept (albeit maybe impossible in practice), but when you look at them closely they present exactly the sort of moral/ontological dilemma you are worried about.This suggests that we do not fully grok even our own concept of personal identity.

One solution, is to conclude that, after much thought, if you cannot define a consistent concept of persistence of personal identity over time, perhaps this is because it is not an intellectual concept, but a lizard-brain panic caused by the mention of death.

In my mind this is exactly the same sort of debate people have over free will. The concept makes no real sense as an ontological concept, but it is one so deeply ingrained in our culture that it takes a lot of thought to accept that.