Size : 10 x sun's mass.
Distance : 1600 LY.
Previous closest had been : ~5000 LY.
For comparison, a star going supernova to harm earth has be to within 70 LY.
Maybe start by shifting the orbit of the whole solar system out-of-plane. (I guess that would be done by electromagnetically stimulating the sun to produce a polar jet for a few million years.) That provides our distant descendants another 100M years to alter the orbit further so as not to just plunge back in on the other side. But even without, the risk would grow back to our present level for only (say) 10M out of each 100M years, strictly an improvement.
Orbital plane maneuvers are infamously expensive in delta-V.
Spending the following 100M years increasing our galactic orbital radius might put us in the outskirts before crossing again, if we did not actually escape entirely.
We might also be able to put off by a few billion years the sun itself sterilizing the planet, using the same apparatus. We could only hope it would not be abused to destroy us itself.
Andromeda isn't due for another 4.5 Gy. Presumably its central black hole and ours will merge shortly thereafter, maybe sterilizing the whole galaxy? I am content to leave worrying about that to others.
what is that based on?
*edit
For anyone interested in this topic I suggest Phil Plait’s book in the subject
500 ly is supposed to be equivalent range for a magnetar quake. I think the nearest known magnetar is around 10x that. But even 1% of the radiation needed to sterilize the solar system would be pretty uncomfortable.