If the models depend on factors which cannot be reliably forecast (e.g. "PDO, AMO, and solar cycles" above), then it is a bit of a fake explanation and you can't use them as reliable inputs to a forecast model. Would it be it reasonable to use Akasofu's sine-wave extrapolation of the multi-decadal oscillation in light of the prior two observed "cycles" ?

Also the Pacific Decadal Oscillation and the Atlantic Multidecadal Oscillation indices are measures of the response of the system, and treating them as a driver of the system smuggles some of the dependent response variables into the supposedly independent predictor variables.