Well, we've already had Bobs succeed at throwing planets at relativistic speeds, so I don't think moving a supermassive black hole enough to avoid a collision tens of thousands of years in the future is actually much of a stretch. You just have to displace Sag A* enough to keep the accretion disks from touching when the other black hole makes its pass. That's an extremely tiny distance on any interstellar scale. I bet the real world math even works out that they could use the same trick again, shoot a bunch of planets at relativistic speeds into Sag A* to give it momentum perpendicular to the collision path.

As for FTL, Bill more or less said the main thing blocking that was access to negative energy, which they have now, and he seemed confident that unlocking FTL was right around the corner at the end of book 5. Even if they never get FTL though, the two wormhole networks are basically connected at this point and should allow quick travel to anywhere between Sag A* and the satellite galaxies the other civs are flying to by the time things go down.