The equivalent of the 60 Hz forcing signal is more complicated in lunisolar terms. The analogy is that there are two strong signals that are nearly balanced but closely spaced at 59 Hz and 61 Hz. These are the fortnightly tropical signal and the monthly anomalistic tidal forces. When amplified by the annual spring barrier, the repeat cycle of just these two signals is at least 130 years(***). Yet, we only have 140 years of monthly resolution ENSO data to deal with (since about 1880).
The equivalent for a tidal signal analysis is someone giving you only 2 weeks worth of tidal gauge data, and then you have to deal with a non-linear fit on top of that. If you want to get the next 2 weeks, you have to wait the equivalent of another 130 years.
You demanding an extrapolated time series without having the slightest idea of how to discriminate tightly spaced signals in the context of a non-linear model is the real issue. Perhaps you want to reconsider what you are asking. That's why I don't care. Perhaps if some other people get involved in the project they can offer up independent projections, and spend the next decade waiting for data to come in.
The bottom-line is that 130 years of data is not nearly enough time to justify punting on the problem and attributing it to a "multi-chaos" mechanism. You and a whole boat-load of climate scientists are apparently not aware of the underlying issue on what otherwise would be a straightforward analysis.
(***) Taking all the orbital cycles into consideration, it may be 1800 years according to Keeling
> "The 1,800-year oceanic tidal cycle: A possible cause of rapid climate change" Charles D. Keeling and Timothy P. Whorf https://www.pnas.org/content/97/8/3814