just move the eath out of the way
Good thinking. Right now tidal drag is pulling the moon away from the earth at 1 cm (about 3/8's of an inch) per century. To accomplish this, energy is transferred from the earth's spin to the moon's orbit at about one gigawatt, continously.
One of the problems with nudging an asteroid away from a keyhole, is that that only postpones the problem. The rock will come back every year or so and eventually will need to nudged again. Perferrable might be nudging them into a collision with the far side of the moon (where debris is less likely to later impact earth).