2. Beam me up

Yes, we do perceive our psychological continuity to be more important than any physical continuity. This is evident in our ideas behind ghosts and of mythological punishments (where sorcerers turned men into frogs, toads and other creatures where the victims knew of their transformation) - the psychological form transcended the physical form. Even modern day films use such hyper-physical identity transformations (there was a movie where a man and woman switched bodies, a teenage girl and her mom did the same - titles of which i can't remember, haha). So, it is agreed that a person heart-mind-soul are more important then their bodies. The body is a container to support these things. As long as the death of the heart-mind-soul is deemed more substantial than the death of the body, then there is no murder. No end or loss of memory, no break in continuity of experience, no end of 'life'.