If you don't use a retrofit series, you'll have to get a mobile spaceyard to the star and start building the ringworld activator containing starbase on this turn, and turn on emergency build just in time, or you won't be able to build a ringworld in time. And that's just for turn based, I don't know if you'd ever make it on strategic.
You really should prepare to evacuate instead. Let the rest of the galaxy feel your pain when the horde of emigrants emerges.
You can try to trade your doomed system for someone else's planets. When the trade is completed and other guy gets your system, they will get no warning messages about the instability, and it will just blow up when the time comes.