I try to deal with uncertainties by routinely going to the higher resolution time series such as the 5-day MJO and daily SOI data sets. So the fits become multi-scale and the uncertainties can potentially be narrowed down.
High-resolution (5-day) MJO model fit
Back extrapolation to historical SOI
The forcing for SOI and high-res MJO is aligned, not degrading at all regions that are outside the training interval (prior to 1980)
The LTE modulation over the entire span (above following) and just over the post 1979 MJO data interval (below following)
Power spectrum of forcing shows the expected 13.66 day tropical fortnightly signal, but nearly inseparable from the next strongest 27.55 day anomalistic monthly signal. With the annual impulse mixing these show up as 3.795 year and 3.917 year periods, which thus gives rise to a long beat frequency of 121 years, which is likely the low-frequency peak.
There's a whole world of signal processing approaches available that has barely been scratched.