That shouldn't be a bottleneck. Let's say the matter is not destroyed and then recreated, E=mcc style - it's merely converted, and thus retains structural information about itself.
I suppose now we're getting down to our definitions of destroyed and recreated. You say that matter isn't destroyed in transport; that it's converted. Converted into what? Energy? A simpler form of matter? And to make this conversion, wouldn't you have to deconstruct the material in order to change it's fundamental properties?
Now, if you're saying that the matter is not deconstructed, that it's merely phased into subspace
, then I could see how it could retain information about itself. Indeed, subspace has been referenced as the method of directing the matter stream. Subspace has also been made akin to alternate universes, which would hold true for how people could step through the looking glass to the mirror universe. All sounds well and good, except...
Thomas Riker and Tuvix come and bite you in the ass. In the former case, matter/energy had to be added, and in the latter matter had to be removed. It couldn't have come from subspace, since the TNG episode "Schisms" suggests that theres a whole slew of problems for matter from other subspace domains existing in our universe for very long. Therefore, it must have been supplied/removed in our reality, and the only way I know for that to happen is if the matter was analyzed by the transporter, the information backed up to a database, the matter is unmade, converted into energy, routed through the subspace antennae, then reconstructed using the same energy that was destroyed using the blueprint originally scanned.
Not really. When she stepped out of the transporter, all she did was stare, and get hugged by Picard. She didn't get a word out of her mouth.
We then cut to a completely different scene, where apparently Picard has brought her up to speed, and the two are discussing the operation. There is no discussion of the events of the past days or hours as such.
In the scene in question, Pulaski walks off the transporter, shakes hands with people. Then Picard takes her by the shoulder and they both walk out the door. The camera changes to outside the transporter room in the corridor, where they walk out the door and continue walking. There is no indication of a time jump or a missed scene. Pulaski then says "Captain, if this hadn't worked...", 'this' being their plan to restore her DNA.