Here is a plot from Chao from that same paper showing the contribution of LOD from various spectral sources. These are all defined by a characteristic frequency:
Going from right to left
1. Semi-diurnal tides --> Tidal forcing
2. Diurnal tides --> Tidal forcing
3. Long-period tides --> Tidal forcing
4. 40-60 day oscillation --> (see below)
5. Semi-annual --> Solar + Tidal
6. Annual --> Solar + Tidal
7. Core --> ???
8. ENSO --> Tidal forcing
9. QBO --> Tidal forcing
10. Secular --> ???
As for the 40-60 day oscillation, I was looking at my ENSO model with high resolution SOI data, and it appears to pick up this variation, with likely a slightly different response function than the longer period >1 year cycles that ENSO is known for.
The greater point in all this is that the vast majority of LOD variations is due to the cyclic variation in the lunisolar forcing. All these other behaviors such as ENSO and QBO that contribute to LOD variations are transitively related to lunisolar forcing as well.
I actually don't know what would be so surprising about such a result, in that the forcing that is required to cause LOD changes likely comes from some external force, and there aren't that many forces to choose from.
The only contribution remaining are from core changes in the mantle of the earth. I suppose that the earth's highly viscous mantle (with a liquid outer core that is much less viscous than the mantle) spinning at the rate that it does could also undergo changes that are ultimately tied to lunisolar tidal forcing.
What's left are slight variations in the LOD due to earthquakes, which truly are noise, apart from the fact that even these are transitively related to triggering by lunar forcing.