Of course, this still doesn't answer anything about knowing the position of stars in the galactic centre or in one of the distant spiral arms that we haven't been to yet...
We can right now, using today's technology build up a model predicting how distant stars and celestial objects will change their position over time.
By measuring things like distance from earth, angular diameter and velocity of the object and comparing those measurements to historical observations we can predict how the object will behave over time.
The reality could be different but the models can give us a pretty good idea of how the galaxy and the position of stars will change over a period of time. As the game is set over 1000 years from now, there would presumably me much more accurate models available which could accurately plot the position of the distant stars.
We can also predict how a star/solar system will evolve over time.. For example, current predictions suggest that Betelguese (Alpha Orionis), which is one of the stars in the Orion constellation, will go supernova within the next few hundred thousand years. We can predict this by observing how the star's mass, luminosity etc. is changing over time. However even if it did go nova there would still be something there, in the form of a neutron star remnant.
Love the thread by the way...