Whoops, I somehow overlooked your Jan 16 post above, with its interesting information. Deterministic Chaos science need not just "punt" at relative computational intractability, with heuristics left to bear.
Coriolis momentum is a leading-order term in both ENSO and QBO dynamics, that could be interpreted as a forcing factor. A plausible effect of Coriolis Geostrophics is to add planetary rotational energy to ENSO-QBO, speeding up frequency like tight-wound clockwork.
Again, I speculate from first principles, not yet ready to settle on comprehensive conclusions. I do think there must be some harmonic tidal forcing, as a higher order, but perhaps far below data and computation available to predict or detect it.
Searching for discussion of Coriolis Effect in your ENSO and QBO posting did not turn up any hits in the first few page results. Thanks for any pointer to that possibly key aspect of the problem.
A recent paper involving Rossby (Coriolis related) gravity-wave QBO associated modulation-
On the role of Rossby wave breaking in the quasi‐biennial modulation of the stratospheric polar vortex during boreal winter [Hua Lu et al 2020]