This does seem extremely far out-there, and more than a bit shaky without more information, but we'll see if anything comes of it.
From a casual standpoint, though, and really I'm in no position to be puzzling over relativity of simultaneity at this hour, I'm not sure that this would run into the causality elephant in the room. At least from the speculation I'm seeing, the bubble of flat space-time inside the drive would essentially be causally disconnected from overall space-time (hell if I know how the physics of that play out). Both the ship and the outside observer would be experiencing the same passage of time, but there could be no communication between the two. I'm not even sure what an observer in any inertial reference frame relative to the ship would "see," because of the space-time warp, but if they couldn't obtain any information from inside that bubble, then I don't think there would be any way to deliver information into the ship's own past.
But yeah, I'll leave it to someone else to pore over a space-time diagram of what's going on.
