I'm certainly not a physicist, but I don't think even artificial gravity will spare you from relativistic effects. If you go fast enough in normal space
then you'll experience time dilation. That's proven science. And if your warp engines are out then how can you create a subspace bubble to take you out of normal space? Yeah, I know they pulled that in DS9's pilot episode, but it's still bullshit.
The only loop hole I can see is that impulse engines can create a sunspace bubble to take you out of normal space and thus save you from time dilation. And even if impulse can get you just a bit faster than light you still have a years to centuries voyage to get back from the galaxy's edge.