but yes, you are right, it should be an astropath that sent the distress signal.
So wait, does this mean in your second concept that the 'accident' takes place in realspace and not in the warp? Or do these Lantern Marines not practice standard imperial safety doctrines of locking up/shielding their astropaths when they are in warp travel?
As well, even the most basic transmission isn't instant and can take hours to send for astropaths. Well, other than a death scream. That tends to be rather abrupt and one of the most potent transmissions that an astropath will ever make in his or her life