>A while back I tried this DiffEq solution to a frequency-modulated wave equation. This has forcing components at 1 year and 1/2 year periods and some from TSI variability

I don't see why the above is supposed to be a TSI variability.
The matching looks again impressive, but then again this is only a finite stripe you are looking at. From where do all those coefficients and the diffeq itself come? I have no mathematica and no feeling what the solutions to this weird diffeq could look like for a small variation of the parameters.