I think the problem with your machine is the way it works.
It's not a teleporter, but a clone and disintegrate one machine you've got there.
I'm not a matematician, but if there is a delay between having cloned yourself, the verification process and the disintegration of your original self, you will for a short amount of time exist as a doubleganger of yourself in two places at the same time.
A teleporter is for me, a machine that actually teleports you, i.e. moves you over a distance. The move doesn't have to be instantanious, just presumably faster, safer, whatever.
For the sake of argument about the definition of the *I*, you might as well just have stuck to a simple clone example. If a machine could duplicate you as a snapshot in time, with matter, exact configuration of electrical charges in yoiur braincells, everything pretty much, which one of them would be the *I*.
You would most likely just go nuts when you are faced with the paradox of being half the person you were before