There must be holes with this, but I think I have an idea for superluminal travel that avoids paradoxes. It involves some silly rules though.
If we imagine only one reference frame (ct,x), then there are no paradoxes with superluminal (i'm thinking instantaneous) travel or communication between "A" and "B".
However, a problem arises when we introduce a second inertial frame (ct',x'). A message could be sent from "B" to "C" regarding an initial message sent to "B" from "A" to prevent the message from "A" to "B" being sent in the first place. A paradox is born.
However, what if we impose one simple rule on superluminal travel/communication?
1. Ansible communication can only be done between devices within the same inertial frame and engaging your ship's jump drive will always drop you out in the same inertial frame.
This prevents a message from being sent from "B" to "C" (from within the ct',x' frame).
I've been developing this idea for a short story I want to write and it's surely taken a while to try to craft a concept of superluminal travel that works with relativity without breaking causality...or so I hope!