Humans leaving the planet could be extremely difficult. Far easier to move the Earth out a ways to keep it in the habitable zone.
Not sure what the energy requirements would be to boost the Earth to a higher orbit around the Sun, but they must be gargantuan. Maybe we could launch a giant "sunshade" to partly block the sun. Make it a solar collector and beam back the energy to Earth as a bonus. (I know, I'm dreaming. The reality is we don't even have an available means to launch a manned vehicle at the moment. Sad, really.)
Back in the Cold War days there was a story that "Red China" was developing a Doomsday weapon: The communist government would equip every Chinese citizen with a six foot stump in their yard. At a signal from Chairman Mao everyone would mount their stump and jump off, knocking the Earth out of its orbit.