Sounds like a good plan to me

What if we didn't sync the earth and moon rotation, but instead when we run the cable from the earth to the moon, we attach that cable to a little train car that runs on a track all the way around the earth? The moon will pull the car around and it would have generators on it to get the electricity.
- I assume the little train car will quickly become a wrecking ball, leaving a band around the earth where you can't build anything and also if you go there you might randomly get absolutely FUCKED by a swinging train car.
  
  I see this as an absolute win, it could have a livestream like the 11 foot 8 bridge

I always wondered what happened to the guy who wrote word problems for high school physics textbooks. Just goes to show you either die a hero or live long enough to become the crack rock

And it'll only take 10^7 years to pay for itself, bargain!
- Will probably be someone else's problem by that time... So why not?
- Show your math or fake news
  
  First section says it'll take 10^{29 joules to slow down the earth, third section says 10}22 joules in 350 days, so 10^7 difference, approx that many years to make back the energy from step 1

Funnily enough making the day the same length as the Moon's orbit is enough to stop the Moon from drifting away by itself. It's actually the tidal forces caused by that mismatch that are causing the Moon to slowly drift away.
Another fun fact: The Earth's day is getting slower due to those forces faster than the Moon is drifting away. Given enough time the Earth would end up tidally locked to the Moon and the Moon would stop drifting away on its own. Of course, they'll both be consumed by the Sun long before that would happen, but I think it's kinda interesting anyway.

I do love that tidal power is actually just moon power. I think we should call it that more often.
- Lunar power, to accompany solar power.

We should just syphon all the water out of the ocean, put it in a giant still and use a massive rocket to move it near the sun.
Now we have unlimited steam energy and way more land to build things on. Winning!