Heuristic Logic is properly a Class of Ansatz, under Category Theory. Its untrue that a successful "heuristic is something that just appears to work but otherwise does not lead anywhere". MathVault defines it better. Like many of my generation, I first learned Heuristic Reasoning from the papers and lectures of Nobel laureate Herbert A. Simon, in the context of AI.
Here is a more correct parsimonious version of your statement: "Sunspots have a roughly 11‐year cycle, making them (quasi-periodic). We do not fully understand the mechanism." No need to abuse "heuristic" in a way that "does not lead anywhere", to then claim its the inherent fault of heuristic logic, rather than poor word choice.
Herbert Simon worked closely on Heuristic Logic with Doug Lenat, whom I studied AI under, at UTexas-Austin. Here Feynman colorfully discusses the power of heuristics by invoking Lenat. Like MathVault's definition, Feynman's is a far more apt description than yours of the heuristic ansatz-
At first blush, the Mars' Chandler Wobble seems to me like a close subharmonic of the beat (ratio) between Mars' solar year and its apsidal precession period. Mars' moons are too tiny, and and their orbital periods too fast, to strongly suggest forcing.
Do you really believe there is no Lunisolar Crosstalk signal possible overlaid on the ENSO-QBO state-data you chart? Its like you can't admit that possibility, much less understand its likelihood, because you reject a priori the heuristic ansatz needed. So you cast about for distractive arguments, but the question stands.