But "travel into the past" does not raise causality issues unless it is into a past prior to the time of the transmission being replied to! That's the whole point: you need a second inertial frame (i.e., a third reference frame) in order to produce that phenomenon (based on current theory).
That's exactly what would happen. Re-read my post 119, where I pointed out:
Now you get on the supspace radio and send your condolences back to earth: "So sorry to learn of the July 4th assasination of President Hillary Clinton." Ah, but here comes the catch. You are sending this message on your July 3d. Because of your acceleration away from earth, from your point of view -- which is just as valid as earth's viewpoint -- it's earlier on earth than it is on your ship. So your message travels instantly and gets to earth on July 2nd. Earth's July 2nd. And they now know of the event before it happened.