I think Gödel's second incompleteness theorem
rules out the possibility of a transporter beaming itself. A transporter needs to model and process the complete
data about anything it transports, nothing left out, but Godel's theorem proves that no system can completely explain or encompass itself. It can only be completely modeled by a larger system that contains it.
And you seem to be saying the matter stream is a Bose-Einstein condensate, but that doesn't mean there's an intact machine in there somewhere. In order for something to function as an intact material object, it needs to have its particles correlated in a macroscopic, "classical" state wherein they're all physically connected into a solid. They need to be in certain positions to work; the particles of the focusing components have to be aligned so that they function as lenses, the particles of the current paths have to be aligned so that they can actually conduct electricity along a path, etc. There needs to be a single definite answer to where the bits go and how they interact in order for them to have a definite effect.
Physical laws apply everywhere, but they have to be directed in the right ways to get a desired effect. A huge pile of sawdust is subject to the same physical laws as a catapult made of the same amount of wood, but it's not going to be able to have the same effect, because it's not in a configuration that can exert or take advantage of physical laws in the right way.