This is all very interesting. I suspect both the inherent risk of overfitting from noisy data that you cite, and also risk of underfitting, from still-incomplete identification of chaotic ENSO multi-physics. Poor predictions either or both ways.
Let me take some time to study and ponder the issues as you present them. Accurate real-world prediction will still be the truest test of your model, of "straightforwardly...tidally forced behaviors" (ie. not highly chaotic). Lunisolar Earth tides start as a three-body system, so chaos is predicted from the start.
Yikes, Vertical Coriolis Effect at the equator seems like a huge source of Earth Rotational Energy to account for, but I am not seeing much in the literature. I suspect ENSO of some sort would occur if the Moon did not exist, and this would be a likely driver. Lunisolar signal may just be a coherent source of noise overlaid on the underlying harmonics, that could be interpreted as "forcing". Take the loudspeaker 60Hz hum case, with 60Hz as the tidal signal, and posit a quasiperiodic lower frequency drumbeat in the audio. 60Hz periodicity could be interpreted as "forcing" the quasi-periodic signal, by observation of superposition.
On a related tack, consider ENSO and tides as planetary-scale phonons that are constantly created and annihilated. A high tide is one phonon, and a low tide is its antiparticle. Similarly, El Nino and La Nina are an anti-pair, and Tidal and ENSO phonons constantly super-pose. In this physical interpretation, heuristically, the Tidal and Coriolis energy hardly interact, although they seem to when compounded into one signal stream.
A terrific ENSO clue is the original observation of Peruvian fishermen of the onset of major change in December ("El Nino"). This is obviously a Solar seasonal year signal, not a Lunar signal. We may posit equatorial oceanic ITCZ flow as a band wandering north and south, seasonally, and that ENSO's state is carried along with it, sweeping the coast. To an observer on the coast, the onset seems to happen suddenly, when the sweep arrives.
A huge problem nailing down ENSO is Heisenberg Uncertainty with regard to its position and velocity. Overlaying the Lunisolar signal on a fuzzy ENSO signal is fraught with imprecision.
Axiom: LaPlace's Demon is smarter than LaPlace.
Commentary: LaPlace would not have stopped at his Tidal Equations to explain ENSO. His Demon could best resolve ENSO's deterministic chaos.