[hirsin]

This may be hopelessly naive but isn't the idea of GR that with sufficient fuel (and I suppose breaking some laws of physics) I can effectively postpone my experiencing next Thursday (here on earth) by moving away from earth at one lightsecond/second?

[ben_w]

Other way around, the more you accelerate, the less time you experience between now and then.

[ykonstant]

And to emphasize the above point, it doesn't matter which "direction" you accelerate towards; the singularity is in the future, and you are approaching the future faster the more you accelerate.