Heuristic Logic is indeed both foundation and summit of math; the most powerful applied math as the most powerful AI paradigm. Historical review of the Philosophy of Mathematics confirms semantic knowledge as the uppermost level of abstraction, not numerist fetishisms. Statistics is quite mechanical, helplessly prone to GIGO, if the heuristic logic assumptions are flawed.
MathVault's "Definitive Glossary of Higher Mathematical Jargon" puts it this way-
"In general, heuristics and algorithms are similar in that both constitute some form of mathematical procedures, but are different in that the former prioritizes higher-order thinking over the actual steps — and as such might require a bit more mental flexibility and creativity."
ENSO-QBO interpretation was at an impasse here, Paul, between you and the NOAA-types. They could not see the evident Lunisolar signal in the noisy data that we see. You could could not accept any logical limitations of your forcing insight, nor embrace applicable nuances of Chaos Theory, as most geophysicists (and I) do.
Now a shiny new hypothesis better explains your charts, based on the same ENSO-QBO data. Lunisolar Crosstalk contaminates sensor data to show up in your plots. You cannot prove only forcing is visible in the ENSO-QBO lunisolar data, with zero crosstalk component. NOAA's folks will gracefully concede a crosstalk component, if you choose to publish that finding.
Go ahead and laugh; its a fine outcome.
PS. The Chandler Wobble is put to rest, having been shown as mostly Lunisolar seafloor tidal pressure, as we agree with, rather than than contest.
ENSO and QBO are quite different animals. A statistical lens into their bulk dynamics is that their parts do not exhibit strongly coherent Bose-Einstein Statistics. The various parts react with varied time signatures, with slower processes effectively as delay-lines. This is another clue that your charts indeed mostly reflect Lunisolar crosstalk, in real-time, without the extended smearing of asynchronous responses.