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The Jerusalem Duality - solution to the transportation destruction problem?

S1E12 "The Jerusalem Duality" begins with the Sheldon talking about the problem with teleportation of the kind Star Trek uses (your molecular pattern is turned into energy, beamed to a new place and reconstituted as a perfect copy) because it destroys you even though from the outside world you appear to be the same.

Consider people who have had their fingers cut off and reattached. Their being is not destroyed in the process. Even major organs can be removed and then put back into your body without permanent harm or destruction of your body.

Imagine being able to place your body in stasis, slicing a one atom thin layer, moving this layer 1 meter to the right, and then slicing the next thin layer, attaching it to the first, and then continue until your entire body has been taken apart and put back together again. Using the surgery example above, it means your body was not destroyed, you're still you.

Now assume molecules can be destroyed, encoded, teleported and reconstituted and we do the exact same one layer at a time thing and beam your body across a vast distance, slice by slice.

Would doing it this way mean you aren't destroyed in the process?