I'm not making up any technology. Conservation of energy, solar power, artificial satellites, and Newtonian gravitation are not the same kind of "science fiction" as faster-than-light drives, little green men, or inevitable human extinction. What we should predict, according to the information we have right now, is that humans will be able to decide whether or not the Earth gets incinerated, unless they die off first.

Yes, moving the Earth is a larger project than replacing CFCs. But the humans harness progressively larger amounts of power per capita over time, historically at the rate of about 1.2% per year. At that rate, a Dyson swarm will capture effectively all of the Sun's 48-petawatt output in six or seven hundred years, though I expect the rate to accelerate. That's over a billion times larger than the power required to move Earth to anywhere. If you were to distribute the Sun's power evenly to the world's current population, only 7 people (per generation) would need to pool their shares to achieve it. So the magnitude of investment is extremely manageable.

I'm not interested in the real and very big obstacles that are in your way right now. I'm interested in which of those obstacles will remain 400 million years from now. It seems irresponsible to speculate that humanity will remain collectively suicidal for such long spans of time—if nothing else, you'd expect the collectively-suicidal subpopulations to become scarcer over time.