PaulP: "Its punting if you claim any of these behaviors is "multi-chaos" since that implies the solutions are intractable."
Agreed, any such claim would be wrong.
No behavior is multi-chaos in isolation, its in the high-order combinatorics. The solutions are not hopelessly intractable, just as Weather prediction is workable to a useful degree. To dismiss hypercomplex multi-chaos a-priori would be "punting on 1st down".
Systems like ENSO and QBO are indeed sensitive in many ways, so volcanic disturbances is just one more factor of note. We can hypothesize that Ice Ages, Large Meteor Impacts, Anthropogenic Climate Change, and many other events can disrupt these oscillators. In fact, the volcanic simulation cited caused "slightly prolonged periodicity", such that lunar tide excitation could not possibly be synchronous forcing.
We do not stop trying to understand and forecast Weather just because its multi-chaos. In fact, Chaos Science helps us better understand such complex determinism. Its the "quasi" in quasiperiodic.