This was a really interesting read, thanks! Is it correct that this doesn't take into account any relative motion of the stars, and instead assumes they are fixed points? I assume the relative velocities are not significant since they're pretty close together, but I'm curious if you investigated that.
The HYG database has the velocity vectors of the stars. These are calculated from proper motion (i.e. the star's movement across the celestial sphere) and radial velocity (measured spectroscopically, by the Doppler shift of the light).
In short (kiloyear) timescales, relative motion doesn't matter, because the stars move so slowly. For Beta Pictoris the velocity vectors are:
0.00001886 parsecs/yr is ~20km/s. At this speed, it would take 10,000 years to travel a mere 0.6 light years. A rounding error.
On longer timescales, the velocity vectors are useless, because it's an n-body problem, and the initial conditions (position and velocity vectors) have massive error bars. Calculating accurate stellar positions in the far future is a task for a group of astronomy PhD's and is beyond my limited skills.
The story timeline is never stated, but it doesn't take place far enough into the future for stellar motion to matter---if you follow the clues you can bound it.
