Larry Niven proposed in his book A World Out of Time moving the Earth by using Neptune’s gravity to drag it around. It goes something like this:
Neptune, being a gas giant, is essentially one giant fuel source. Build a fusion motor that floats in it’s atmosphere and fires repeatedly (like the pulse jet engine of the old german V-1). The relatively “gentle” love taps wouldn’t kill anyone since they were happening on Neptune, not Earth. You drive Neptune down closer to the Sun and drop it in front of Earth. Neptune’s gravity tugs on the whole planet at once (Neptune is big enough that the tides, while not negligible, are not likely to slosh the oceans around too much). Accelerate Neptune again and it’s gravity drags Earth along. Once you get Earth where you want it, you pour on the acceleration and Neptune pulls away, leaving Earth snug and safe in a new orbit. You leave Neptune wandering around the outer system so you can use it again, the next time you need to move the Earth.
In Niven’s book, Earth is moved out a couple of times, at one point being in Mars’s orbit (at Mars’s L3… opposite the Sun). Eventually, Earth is moved out even further and is left orbiting Jupiter (finding a balance point where Earth is not too hot nor too cold is complicated by Jupiter’s orbit, so put Earth in orbit of Jupiter and then warm Jupiter up a little bit so Earth stays comfortable).
Science fiction is fun.