Assuming we've "defeated" natural selection, or at least made it slower, humans will still be relatively the same. This is in comparison to the rest of life on Earth, which we assume will evolve at the same and/or faster rates as they always have. So the animals that you're talking about "saving" will have spent millions - billions? - of years adapting to the slowly changing environment. Rapidly moving the earth would change everything - tides, gravity, the length of the days and years - would just result in mass extinction anyway.