A variance in the rate at which the Moon orbits the Earth is most likely due to the Earths own procession which has varied throughout it's existence.
The procession of a planet doesn't affect the rate at which a satellite orbits it if the distance between the two bodies remains constant. That being said, the Earth-Moon system is much further apart now than it was 4 billion years ago.
It like saying the electron's plasmic cloud is fixed and there is no evidence for that, ss we know with the discharge of photons from energy levels nothing is fixed at a preferred rate.
The location of electrons in an orbital is not fixed, but the amount of energy they have most certainly is. The consistency of the energy levels in the absorption spectra of particular elements regardless of when and where they are measured is a testament to this. An electron in its ground state in an atom will remain at a constant energy level unless an outside interaction changes it (such as the formation of a molecular bond or the absorption of a photon).