I will be finishing up the basic research on my ENSO model soon. I don't have many loose ends left and what I presented at the AGU is standing the test of time. The Chandler wobble is tied to the aliased draconic month cycle so I can essentially get perfect agreement by applying Laplace's tidal equations with the known seasonally reinforced lunar forcing. The ENSO fit then has only amplitude and phase unknowns with regard to the 3 lunar monthly cycles, making it conceptually identical to an ocean tidal model fit. The complexity is similar to the ocean tidal setup with the 3 monthly cycles combining with the 2 seasonal cycles (yearly and biannual) to create 18 linear and nonlinear interactions.
I performed a long running fit to the ENSO time series by allowing the lunar cycle periods to vary and then waiting for it to converge to steady state values.
Draconic month (strongest) should be 27.2122 days
Anomalistic month should be 27.5545
Sidereal month is 27.3216
What the model converges to is 27.2120 days for Draconic
27.5580 for Anomalistic
27.3259 for Sidereal
These errors are less than a minute per month in the case of the Draconic and 5 and 6 minutes for the other two. The latter error contributes less than a quarter of a lunar month phase shift over the 130 year ENSO interval.