The Canis Major Dwarf Galaxy is only 25,000 ly from Earth. Assuming constant acceleration, and sufficient technology to protect and keep things running for all that time - no mean feat - reaching a substantial percentage of light should make that reachable within a hundred or so thousand light years, even with a flip and slow-down halfway.

Seque 1 is only 75k ly.

Andromeda is much farther; I didn't catch it in the article, but I got the impression the strands were identified between the more local clusters.

Wouldn't the ship itself perceive a lot less of that time compared to an external point of reference?