Shen, Wenbin, and Cunchao Peng. 2016. “Detection of Different-Time-Scale Signals in the Length of Day Variation Based on EEMD Analysis Technique.” Special Issue: Geodetic and Geophysical Observations and Applications and Implications 7 (3): 180–86. doi:10.1016/j.geog.2016.05.002.
Because of the law of conservation of momentum sloshing can change the velocity of a container full of liquid, momentarily speeding it up or slowing it down as the liquid sloshes back and forth. By the same token, suddenly slowing or speeding of that container can also cause the sloshing. So there is a chicken and egg quality to the analysis of sloshing, making it difficult to ascertain the origin of the effect.
If ENSO is a manifestation of a liquid sloshing in a container and if the length-of-day (LOD) is a measurement of the angular momentum changes of the Earth's rotation, then it is perhaps useful to compare the fundamental time-varying signals in each measurement.
First let's review the ENSO frequency factors. From the latest ENSO summary post, we find strong values at 14.0 years and 6.48 years, only slightly weaker at 18.6 years, and several corresponding to aliased lunar tidal periods. The lunar month periods of 27.21, 27.32, and 27.55 days result in aliased values which are balanced around a 2 year period are the strongest of that set. Based on the detection of an underlying strong biennial modulation, there are interesting concordances linking the longer periods to the quasi-biennial periods, e.g. the 14 year period multiplied by a 2-year sinusoidal waveform will result in periods of 2.33 years and 1.75 years, which is close to the aliased Draconic or nodal lunar values of 2.37 and 1.73 years.
For the LOD factors, Shen & Peng provide the frequencies and amplitudes of different ΔLOD sinusoidal factors,shown below. They find the expected tidal periods in the signal and longer period factors as well.
Interesting that they don't associate the 9.13 period with the well-known tidal period of 9.133 days  which results from the non-linear interaction of 27.55 and 13.66 day tides, suggesting instead that it is a solid-earth tide.
The actual decomposed time-series are shown in Figure 2 below. Note the obvious ~18.5 year modulation in IMF2 below, which more than likely derives from the well-known nodal declination oscillation  of 18.6 years.
The frequency spectra are shown in Figures 3 and 4 reproduced from Shen & Peng.
What is most remarkable is the association of (1) the LOD signal of 13.69 years with the ENSO signal of 14.0 years, (2) the LOD signal of 6 years with the ENSO signal of 6.48 years, and (3) the QBO related aliased tidal signals spread around a 0.5/year (biennial). There is also a weaker ENSO signal around 47 years, which is resolvable from the 130 year record. The non-aliased tidal signals are not resolved in ENSO because they are less than the monthly sampling rate, while the yearly signals have been filtered out.
Bottom-line is that this analysis of Shen & Peng supports and certainly does not contradict the original ENSO sloshing model. It is also supported by the Chao et al LOD analysis  who further establish a strong 18.6 period based on a wavelet analysis. Having a trio of (14, 6.5, 18.6) values plus tidal values apparent in both LOD and ENSO is likely more than coincidence.
In practice, the ENSO analysis may provide a more accurate resolution in the underlying periods, as it extends for more than 130 years, compared to the 50 year run of the LOD measurements. As a previous post demonstrated, these strong periodicities are evident in the 1880-1950 interval, which accurately project to the 1950-1914 interval, with the correlation coefficient actually higher on the latter interval! So whatever set of periods have been in place based on Shen & Peng's analysis starting in 1962, they likely have been there before that time as well.
And the fact that Hanson & Brier found significant 13-14 year and 6.75 year signals in ENSO going back to 1525, suggests or at least infers that this is an extremely stable feature of both ENSO and LOD.