I don't understand what you're getting at. It would be trivial for someone close by to match that reference frame, and then what?
And then nothing. :-)
My point is that being able to go FTL relative to distant stars does not allow time travel relative to distant stars, which means that there is no possibility of causality violation.
Being able to go FTL in 2 arbitrary reference frames leads to potential causality violation.
Feel free to express yourself in more technically/mathematically: while GR is certainly not my field, I took classes in grad school that covered the material.
In SR, if A and B are two events and B is outside of the light cone of A, then reference frames can be found where A happens before B, A and B happen at the same time, and A happens after B. Therefore FTL travel in one reference frame is traveling backwards in time in another.
The ability to travel FTL in a single preferred reference frame is not sufficient to cause causality violations. That is because all trips move me forward in time according to the preferred reference frame, so I can't wind up at the same time and place that I (in my personal history) was at before. But if I can travel FTL in my choice of reference frame, in my choice of direction, then I can plan a trip from A to B which is FTL in one reference frame, then switch and travel from B to A FTL in a different reference frame. From the original reference frame I first traveled FTL, then backwards in time. In the second reference frame I first traveled backwards in time, then FTL. But both agree that two copies of me wound up at the same place at the same time, and I can try to violate causality.
Suppose that you go from SR to GR but are dealing with a large region that is approximately described by SR though locally it may look different. In my "warp drive" there is no local FTL. But the observations about SR, reference frames, and simultaneity still hold between two distant locations. The ability to warp as fast as I like but only relative to one "approximate SR reference frame" does not let me violate causality. But the ability to do it in any direction relative to any reference frame that I like, gives me the ability to construct "closed time-like loops". Which is what is required to try to violate causality.
Note that I say "try". It is possible that a unified theory of GR and QM could allow for closed timelike loops, but (thanks to quantum decoherence) would not allow you any meaningful interaction with the previous copy of you.
all the machinery of the SR is valid only on the background of the fixed spacetime. Once you start to massage the spacetime itself, the SR is only approximation which is good only to the extent of how good fixed spacetime model is approximation of your real spacetime.