What do you mean by "simultanously"? You've used it to refer to events which do not occur at the same place.

The details are not significant. Simultaneously in the rest frame of earth. Whatever. Or send a timing signal from Mars to Earth at the same time as the radio message is emitted toward Alpha Centauri, then leave Earth when you receive the timing signal. You'll still arrive before the radio message, even though you've given it a head start.

I think that you've shown that the distance between your departure point and Mars is six light years;

The distance between Earth and Mars is 225 million km on average, or 12.5 light minutes.

If you like, you can send your radio message from the same location as your departure point. First emit a (directional) radio signal from earth toward Alpha Centauri. Then depart in your spaceship, just making sure not to collide with the radio signal on your way there (go a different way, say by taking a pit stop at Vega). You'll still get there before the light signal.

you've done that by moving space around such that the point you departed from is in the vicinity of Alpha Centauri.

In a sense, yes, that is exactly what an alcubierre drive is meant to do. The trajectory that starts at Earth, enters the bubble, sits there a while, exits the bubble and arrives at Alpha Centauri travels "locally" less than six light years. The bubble train might be analogised to a wormhole in that it establishes a shorter path between two otherwise distance places.

But unlike a wormhole, the Alcubierre drive doesn't require you set up the path and destination in advance (unless Krasnikov is right, and there aren't any tachyons), and it's an effect confined to the vicinity—in space and time—of the ship using it. So in all meaningful senses it can reasonably be described as a faster than light drive, as opposed to a bridge, which is what a wormhole is.

The radio signal and the ship leave from points that are near each other in the space-time metric. In other words, simultaneous from a reference frame in which they are physically close.

You've moved space around, but only for a small local (space-time wise) area; you haven't permanently moved the two stars closer together.

Er, I think you were substantially less clear than you seem to think you were.

Let it be known henceforth that for all X (where X includes 'wavefronts that are propagating out from you in all directions') when I do not mention X and where a claim of X by myself is actively ruled out by multiple comments of mine and would be a trivial contradiction of basic physics (well, comparatively basic physics) then I do not claim X.

The "That's not a straw man, you just aren't clear" social move is rather flexible, particularly when used in response to even moderately subtle goalpost-shifting. (ie. By default it will be supported and assumed to be pro-social by all those who are not interested or have not been following the context.) Nevertheless, I consider it safe to say that those who read the context and still believe that this comment can be legitimately interpreted as a valid reply to the previous comments is sufficiently poor at keeping concepts distinct as to be way out of their depth when trying to comprehend the implications of novel, probably counterfactual physical phenomena such as Alcubierre drives.