I have been on a path to understand ENSO via its relationship to QBO and the Chandler wobble (along with possible TSI contributions, which is fading) for awhile now. Factors such as QBO and CW have all been considered as possible forcing mechanisms, or at least as correlations, to ENSO in the research literature.
Over time, I got sidetracked into trying to figure out the causes of QBO and the Chandler wobble hoping that it might shed light into how they could be driving ENSO.
But now that we see how the QBO and the Chandler wobble both derive from the seasonally aliased lunar Draconic cycle, it may not take as long to piece the individual bits of evidence together.
I am optimistic based on how simple these precursor models are. As far as both QBO and the Chandler wobble are concerned, one can't ask for a simpler explanation than applying the moon's Draconic orbital cycle as a common forcing mechanism.
As a possible avenue to pursue, the post on Biennial Connection from QBO to ENSO seems to be the most promising direction, as it allows for a plausible phase reversal mechanism in the ENSO standing wave. I'll keep on kicking the rocks to see if anything else pops out.