My favorite private speculation about the possibility of FTL makes use of the six (or is it seven?) "extra" dimensions current in string/M-theory to take a short-cut from one point in our space to another without moving along the time axis... I also realize that the energy required to "unfold" one of those extra dimensions, let alone three of them, would be prohibitive.

Anyway...

if you flip a coin see it land heads and send out a radio message saying “the coin landed heads” then immediately transported a light hour away and sat in your ship waiting to receive your broadcast, you might receive a broadcast that said “the coin landed tails” . The reason being that the point in space time you teleported to hadn’t made the heads/tail split when you got there…

Your coin-flipping experiment hangs on the tail of Schrodinger's Cat, by postulating that the result remains in an indeterminate state for distant observers until its "event horizon" -- that is, the wavefront of photons reflecting off either the head or tail of the coin in your hand -- reaches them and is observed. However, you've already observed the event yourself, then sent a message about it, then jumped in your simultaneous-translation device to skip out a light-hour ahead of three wavefronts: the event's, followed by your transmission, followed by your leaving your lab.

Meanwhile, let's say you already have a colleague stationed one light-hour away. She knows that, at a certain time, a coin will have been flipped; it will either be heads or tails, and you will arrive (physically) at her location before the message you've sent about the coin's resultant state. She also knows that, when you arrive, you already know the coin's state -- you have, in effect, transmitted the information about the result at a velocity exceeding c by carrying it with you in memory. Because the coin-flip has been observed (unlike the dead/not-dead cat), the message received cannot be other than what you know to have been true when you left the lab ...

... as long as your simultaneous-translation device (STD? hmmm, better use a different name for it) does its thing within the same universe.

There's nothing at all wrong with using your experiment to begin a story in which the experimenters discover thereby that they can't go home again. There's a lot you can do with their reaction to that knowledge... you could even have them prepared for the possibility, and go from there.

So many Universes, so little Time...