I guess the timescale was picked up to match the expected end of Sol's main sequence (in ~5 billion years) and its growth into a planet-engulfing red giant, in

I guess the timescale was picked up to match the expected end of Sol's main sequence (in ~5 billion years) and its growth into a planet-engulfing red giant, in which case continuing with the model beyond the next order of magnitude becomes unrealistic. IIUC the instability time scatter plot shows that GR basically stabilises our local N body problem by one to two orders of magnitude in time scale (10^8~10^8.5 vs 10^9~10^10), IOW giving a 900~9000Myr extra vs being derailed by a Mercury-Venus collision in ~100Myr, which would indeed comparatively be "shortly thereafter" at these timescales. I did chuckle at the phrasing though. (Disclaimer: not my field either, so I may be 10^10 wrong)