I understand that the moon causes a tidal bulge on Earth, and this tidal bulge moves slightly ahead of the moon due to Earth's rotation.
When reading about why the moon is moving away from the Earth, the most common explanation given is that the tidal bulge slows Earth's rotation and the moon must speed up due to the conservation of angular momentum. This is a poorly worded explanation as it completely skips the part about what is the mechanism of angular momentum transfer. It assumes that we defined a law and the universe must follow it. No, we found that momentum is always conserved in nature, and we noted it as a law.
Upon digging further, I found the most common explanation for the mechanism of angular momentum transfer is that the tidal bulge exerts a gravitational pull on the moon and speeds it up.
The question that is driving me crazy is that higher orbits are supposed to be slower, not faster. If the moon is speeding up, it should fall closer to Earth rather than move away. The moon must be slowing down if it is moving away from Earth, gaining gravitational potential energy and losing kinetic energy. What am I missing here?
How does the transfer of angular momentum lead to reducing kinetic energy and gaining potential energy? What is the mechanism of action here to cause this?