PaulP: "One man's noise is another man's signal"
MDL (male dominant language) is worse than too many CAPS. "One's noise is another's signal," is better. The science of signal and noise is only begun by quoting this truism.
Your choice of noise in the ENSO data case is all the squiggles in the data that do not fit your Lunisolar Forcing hypothesis. In deterministic chaos science, these are deterministic signals you have not identified. ENSO data from mid-ocean sea-buoys, with kilometers of anchor rode, in fact encode lunisolar noise that you are presume without rigorous diligence to only consist of ENSO forcing signals.
Of course NOAA filters noise, or puts it back in, as seen fit. To their credit, they identify both annual noise and signal in sensor data, where you seemingly can only see signal. Ideally, both signal and noise are accounted for. Only you seem adverse to identifying any tidal noise in ENSO sensor array data, as "marginalizing" to your thesis. Everyone else cited here, including NOAA and me, accepts BOTH Lunisolar Signal and Noise in geophysical data. Your thesis is not well-posed as an all-or-nothing question. Diligently identifying and filtering tidal noise from ENSO data will refine your results.
QBO Data seems to be mostly daily Sonde samplings (plus incidental volcano aerosols, and other clues). Atmospheric-Tide would therefore be a noise factor to the Sonde data, inviting misinterpretation as QBO forcing. Again, the Lunisolar signal is quite sharp semi-cancelling pulses (daily peaks and troughs), but the long period ENSO and QBO states are very fuzzy blobs. You claim these sharp events line up with the fuzzy states, with a precision that is not possible for blobs.
This is a fantastic interactive QBO data presentation-
It looks like there must hidden vertical convections that segment QBO, not just a monolithic ring over the equator. Sure enough, Jupiter QQO photos show discontinuities. The cross-equatorial line vortices assume a herring-bone pattern, with vortices anchored in adjoining circulation bands, just as I suggested early in my discussion here of QBO.