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.
One of the main arguments in how to differentiate the twins in the twin paradox is that the twin subjected to the inertial forces of acceleration is the one who experiences the time dilation. On the other hand, the one who doesn't experience those forces does not experience time dilation.
Inertial dampeners would eliminate the effects of acceleration, and therefore by the principle of equivalence, mechanics aboard ship would operate as if there were no acceleration due to the impulse drive. Therefore, any effect of time dilation would be canceled, as long as the inertial dampeners continue to operate.