Interesting questions. I wouldn't mind shaving off some of that ability to suffer of my own, if I copied my mind and killed the original me(With some adjustments :D), would I still be me?
My assumption is that currently, you are the arrangement of particles and matter in your mind. If you create a second copy of you, that is not you, it is a copy. It isn't made of the same matter, and both machines can exist at the same time. The only way to really "transition" is to do the same thing that we do in real life as our minds develop. Slowly replace and reduce the cells in the mind with artificial ones, and have a slow transition that lasts over years. That way there can never be a "copy" of you, and "you" are defined as the half-half being during the transition period.