Sure it is; if FTL travel turns out impossible after all (hardly a verdict set in stone; geocentric model of the Universe ruled the city for the good part of Common Era, whereas general relativity only recently entered its second century on the dog watch, and dark energy/dark matter epicycles already show the cracks under the heap of postdoc papers), then transfer of civilizational matrix via mind uploading probably should be considered optimal. Moving the Earth or Solar System as the whole may become a task of purely sentimental value. However, we can't exclude a possibility of astroengineering the Sun itself, e.g., via insertion of an artificial black hole into its heart.

Charlie from Stephen King’s Firestarter would be helpful… she felt herself almost in the right mood to change the Sun, once.