In trying to isolate the Chandler wobble mechanism, Grumbine seems to agree that it has something to do with external forcing, but rules out lunar because books on the earth's rotation by Munk and Lambeck rules that mechanism out.
> "Gravitational torques have been examined previously as the main driver of the Chandler Wobble and rejected [**Munk and MacDonald , 1960; Lambeck , 1980**], which means only non-gravitational external forces, such as earth-sun distance, force Chandler Wobble at these periods, if any external sources do." http://moregrumbinescience.blogspot.com/2016/01/earth-sun-distance-and-chandler-wobble.html
I can see this hypothetically if the earth was a perfect sphere, since there is no moment of inertia to torque against. But the earth is not a perfect sphere, so triaxial moments exist. It is also well-known and not contested that the moon will perturb the Earth's rotation rate based on decades worth of LOD (length-of-day) measurements. Changes in LOD perfectly align with tidal periods.
Yet the only mechanism acknowledged for *forced* precession is this very long period torque
> "The free precession of the Earth's symmetry axis in space, which is known as the Chandler wobble--because it was discovered by the American astronomer S.C. Chandler (1846-1913) in 1891--is superimposed on a much slower forced precession, with a period of about 26,000 years, caused by the small gravitational torque exerted on the Earth by the Sun and Moon, as a consequence of the Earth's slight oblateness." https://farside.ph.utexas.edu/teaching/celestial/Celestial/node72.html
This is the beat difference between 365.24219 and 365.25636 days, the tropical and sidereal years. Every 26,000 years an extra tropical year is gained.
I think they just overlooked the possibility of the lunar month physically aliasing with the yearly forcing creating the same period as the Chandler wobble. The lunar month was rejected long ago because obviously the periods don't match. But they match if the seasonal aliasing math is done correctly.