> If the Moon were in LEO this process would be reversed; the Moon would be spinning up the Earth while losing orbital velocity.

The situation is not reversible like that. Angular momentum is linear, but energy is to the power of two.

So there is more energy than momentum here. You loose energy from fictional heating on the tides and energy as the rotation of the earth "pushes" the moon away.

But if you reverse it than as the moon slows down, it goes lower, but as it does so it orbits even faster than before, meaning it would have to speed up the Earth even more.

So rather than having extra energy (i.e. heat) you don't have enough, so instead of tidally locking to the Earth, the moon just gets faster and faster and then crashes.