> "The predicted sensitivity is of a nature that a slight difference now in conditions can completely alter future quasi-periodicity inflection, the longer the time-frame, the more divergent. "
Nope. Doesn't work that way. For example, all indications are that the more the QBO measurements accumulate over time, the closer they converge (NOT diverge) to the theoretically predicted asymptotic value.

That's the definition of a boundary-value problem, not an initial-conditions problem.
ENSO is even more rigid in following a boundary-value problem since the greater inertia of the Pacific ocean volume is less susceptible to perturbations. Same for seasonal cycle. Same for daily cycle. None of these diverge over time,