Excellent long-term solution. One might also note that cable is relatively cheap, and the moon is a quarter the diameter of the earth, and if one can do it once, why not do it again? The image of a flower comes to mind: petals radiating from the center, or more accurately an orange supporting numerous needles, say 30, equidistantly located around the orange's circumference at the lunar equator. Thus multiple pumps working continuously say - every day - in a 30 day cycle. Given Niven / Pornelle like Motie societal collapse, those that look to the moon will see the evidence of our past technological prowess - as of course we shall mount giant reflectors on 15 cable ends that flash at the earth twice a month - like a clock ticking off the days above our heads. well almost, The cables would of course be slightly off-set alternately up to 7 degrees north and south so that a fall would not take the others out. So the true appearance would be a four part spiral, two north and south on the dark-side, two north and south on the light-side (for reference). Given calculation in period actuation, one could also very slowly use these pumps to change Earth's orientation in the galactic plane. Over time, one could theoretically move the earth in a Pluto-like orbital inclination, so that the Earth only passes though the plane of the ecliptic twice a year; thus, reducing long-term probability of asteroids or comets impacting the Earth.As long as we are dedicated to tugging, why not tug up, down, right, or left, as well on the way out? Want a longer year? Possible. Want a shorter year? possible. We know that the moon moves away form the earth about 3.8 centimeters a year due to tidal whipping, given the oceans tidal pull, which slows the earth's rotation and speeds up the moon - thus causing the drift away from earth. We could also effect this similar tidal whipping in accelerating up the Earth / Moon system, potentially additionally transferring the naturally occurring 3.8 centimeter drift to the tug. The end result might be for example 30 hour day on Earth ( finally time enough to get those chores done aye!) and a year that might have another week in it - potentially, thus using both tug and acceleration to move the earth, a two in one movement. Given the millions of years to effect this "lift", life would slowly adapt or evolve to the lengthening day and yearly cycle, as it has done since life began on this planet. Additional benefits are 30 elevators allowing the commerce sure to come by 2452, so the Infinity Engineers can demonstrate the ring thingy, in chapter 7. LOL
I have since thought of one problem (only one?) with this: Jupiter may have a few things to say if we start trying to push the Earth out of its resonance orbit. Meantime, only a hundred million years? I'd better go walk the dog now!