I don’t think its so difficult to convince people. The first individuals might be a problem, but as soon as you get the idea accepted by the scientific community, the rest will follow like lemmings. Some how most humans are very sensitive to the opinion of the majority, especially that of the scholars. I think your objective can be compared and is very similar to the message of atheism, “god does not exist” in a world and time where most people believe in some sort of god.
Similar as with discussions mixing science and religion, the key is mixing up the difference between how, and why questions? Focus on the hows, like science:
How does the teleporter work?
It reads and disassembles the atomic structure of a person, and build an identical structure in a different place. Technically atoms of a particular element are defined such that nothing happens if you replace it with an atom of the same kind. If now in your body you replace half of the atoms instantaneously with atoms of the same kind you would not even notice it. Lets go one step further, lets replace all atoms of your body with other ones instantaneously. You would not notice it. Ooops! Sorry, I just replaced all your atoms, sorry I didn’t ask you for any permission (my finger slipped on the red button). But did you notice? Do you mind? Even if you do, can you prove that I did it? Just joking, I didn’t do it. But I can’t prove that I didn’t do it, neither can anyone else proof if I actually did it or not. So now imagine the same feeling as you have now, (no difference right, (I hope your head got back at the same place as it was 1 minute ago). Now in stead of a long long bus or plane ride, think about the time you can save traveling like this, to another place. Surely it must me more comfortable that sitting in a chair with limited leg space for a couple of hours, let alone cryogenic travel for years, the defrosting really gives a bad headache.
If you look at it scientifically, what are you? Just a bunch of atoms, that grouped up in molecules follow the laws of physics that are the same for everybody. The only thing that makes you you is their configuration. Your feelings and personality are just saved by the connections in your brain. Well this new means of transportation, transports the exact configuration. It is like lossless compression, you know like a zip file. Now we will just transport you in a zip file and use the atoms at the destination, in stead of the atoms here, its really much cheaper faster, and more sustainable in energy terms. There is no difference between before or after. We have an uninterruptable power supply backup system, at the departure site and at the destination site. Nothing that can go wrong.
So the point is, that if you look at it from a how-perspective you there isn’t any difference between the perfect copy of you and you, except that it has a translation and optional rotational (to avoid headache at arrival) transformation on the configuration of your atoms. Now if you or one of your travelers still think, that they are dying some how during the atomic disintegration process at the location of departure. You are probably some religions kind of person who believes, or sometimes doubts about mysterious concepts such as an immaterial soul or something silly like that. If that is the case, or if any way you are still scared to die for whatever reason. Please sit down, take a deep breath and continue.
The main message to understand this way of transportation is: You don’t exist! That is, the you that you think that would die, does not exist for all the same reasons why god does not exist (it is simply not necessary to include such ideas in the theories of physics and science).
Trust me, I am an engineer. We "copy*/translate" the exact atomic configuration, we even tried it with exactly the same atoms, during the proof of concept stages of the design, of course with a small time delay, but it made no difference, same atoms different atoms, you are you. You are just the configuration. It is really just like a computer moving a file from one hard disk to the other.
If then there are still groups of people refusing to believe this, you can try to organize that the government organizes some extra chapter in the physics books, explaining that there is really no reason to believe that you are anything else than just a particular configuration of atoms. You can have some scientist writing books about it for the lay audience, with a picture on the cover where they are sitting in front of a lot of books. One of this books could be called “the me delusion”. Really it’s a piece of cake within 100 years, 80% of the people get used to the idea, just as with atheism.
EDIT: *I am not sure how the no-cloning theorem, and no-teleportation theorem, and entanglement-assisted teleportation for quantum states are of practical relevance on the teleportation of humans or living matter. I understand that one could not observe a quantum state without interfearing with it, but disintegration process could be an observation process determining the quantum state. If quantum states are relevant, Copying is not possible, but the main idea of dying does not depend on copying, it would be of equal importance for moving/teleporting.